\documentclass{article} \usepackage{axiom} \begin{document} \title{\$SPAD/src/input mapleok.input} \author{Timothy Daly} \maketitle \begin{abstract} A set of test results that fail for Maple was published as a database on the web by Vladimir Bondarenko. We looked at these equations in detail, redesigned and rewrote them for OpenAxiom where the equations could be applied, and ran them thru the OpenAxiom system. These are the set of results that give answers in OpenAxiom along with a summary of the tests. \end{abstract} \eject \tableofcontents \eject \section{Result} I've been working for some time to construct a Computer Algebra Test Suite (CATS). The idea came about because it is clear that there is a lack of time and attention on cross-platform testing. We should have available a range of problems with associated math theory and verified results that every computer algebra system can use for testing purposes. To this end I've been collecting test suites from various computer algebra systems and running them thru OpenAxiom. The lastest collection is the Maple bug list posted by Vladimir. Of course there is no common syntax and so one of the problems is that every integral has to be hand-written to match the likely semantics of the original. This is a time consuming effort. pFurthermore there is no general mechanism for collecting results (although I have been looking at automating regression testing in OpenAxiom) so result collection and summary are also hand operations. Nevertheless, the process has completed the first phase of testing and I've attached some summary statistics. Detailed results will be included with the next release of OpenAxiom. For the next phase I've built a special purpose version of OpenAxiom with instrumentation in all of the integration routines. I plan to classify each integral and associate it with the code as part of the literate documentation. This will give us a basis for finding bugs and corner cases. It will also give us working regression test cases. \subsection{Breakdown by category} There were 4865 integrals tested. Of these \begin{itemize} \item (5 0.10\%) Missing Functions \item (1206 24.78\%) Undefined Special Functions or untranslated functions \item (84 1.72\%) Mismatched signatures of existing functions \item (158 3.25\%) Badly Behaved Integrals \item (7 0.14\%) OpenAxiom Internal Errors \item (279 5.73\%) Risch Algorithm Boundary Cases \item (2331 47.91\%) Failed results \item (490 10.07\%) Successful Results \item (305 6.27\%) Indeterminate Results \end{itemize} Of the 4865 integrals the first three cases would not run. That leaves 3570 tests. Of these there were 3097 (73.38\%) integrals that had a potential pole in the path of integration making them rather more difficult to compute. We further break down the results. The number in parentheses is the number of integrals of this class. One observation is that a large number of these integrals involve the signum function. OpenAxiom does not have an integrable form of this function. Frankly, I'm not sure how to integrate functions involving signum. It is hardly a surprise that Maple gets these wrong. On some of the functions I've given example integrals that exhibit the behavior of their category. OpenAxiom has a robust implementation of the Risch algorithm done by Barry Trager and Manuel Bronstein. Still, there are some corner cases that are not implemented. We collected these under a separate category so they will be useful for people who want to investigate extending the algorithms. It is hardly a surprise that Maple finds these hard to do. These tests have uncovered 3 internal errors involving a total of 6 of the integrals. These will be investigated and fixed in a future release. Testing continues on the results that did not complete. Raising the maximum time limit to 10 minutes has generated additional results. \subsection{Missing Functions} These are apparently bogus function names. \begin{itemize} \item (1) f \item (1) op \item (1) product \item (2) elt \end{itemize} \subsection{Undefined Special Functions or Untranslated Functions} Maple has these functios in different forms than OpenAxiom. Some of the special functions have equivalent OpenAxiom representations but Maple is much stronger in special functions. OpenAxiom has single-argument forms of some of these functions but the translations were not clear. \begin{itemize} \item (2) airyAi -- 2 argument form \item (1) airyBi -- 2 argument form \item (2) argument \item (57) atan -- 2 argument form \item (26) ceil \item (2) chebyshevT -- with fractional first argument \item (1) chebyshevU -- with fractional first argument \item (5) conjugate \item (8) Chi \item (78) csgn \item (19) Dirac \item (11) Ei \item (2) EllipticE \item (9) EllipticK \item (4) EllipticPi \item (1) erfc \item (23) floor \item (3) frac \item (30) FresnelC \item (3) Fresnelf \item (1) Fresnelg \item (26) FresnelS \item (3) GegenbauerC \item (6) HankelH1 \item (8) HankelH2 \item (22) Heaviside \item (2) hermiteH -- with fractional first argument \item (1) hypergeom \item (4) KelvinKei \item (4) KelvinKer \item (4) KummerU \item (3) LambertW \item (2) legendreP -- having 3 arguments \item (4) LegendreQ \item (15) LerchPhi \item (2) MeijerG \item (31) polylog \item (34) Psi \item (1) Re \item (1) RootOf \item (25) round \item (2) Shi \item (3) Ssi \item (669) signum \item (11) StruveH \item (10) StruveL \item (12) trunc \item (13) Zeta \end{itemize} \subsection{Mismatched Signatures Of Existing Functions} OpenAxiom's integration routines return a Union of several types. In order to use the result in various other operations one branch of the Union needs to be chosen. I have not done that here so these are listed as though they were special functions with a missing signature. \begin{itemize} \item (1) + \item (7) * \item (1) / \item (1) log \item (73) integrate \item (1) abs \end{itemize} \subsection{Badly Behaved Integrals} \begin{itemize} \item (158) integrate: pole in path of integration \end{itemize} \begin{verbatim} integrate(legendreP(0, z)/(z^2+3*z), z= 0..3,"noPole") \end{verbatim} \subsection{OpenAxiom Internal Errors} \begin{itemize} \item (1) internal error \end{itemize} \begin{verbatim} >> Error detected within library code: (construct (= left 0) (= right 2)) is not a valid isolation interval for (+ (+ (- (** ? 4)) (* 2 (** ? 2))) -1) \end{verbatim} \begin{verbatim} in961:=integrate(log(z-1)*z/(z^2-1)^2, z= 1..%plusInfinity) \end{verbatim} \begin{itemize} \item (4) Cannot take first of an empty list \end{itemize} \begin{verbatim} integrate(sin(z)*csc(z)*(1-1/(%i*z)^(1/2))^(1/2), z= 0..1,"noPole") \end{verbatim} \begin{itemize} \item (2) The function * with signature hashcode is missing from domain Polynomial(OrderedCompletion (Integer)) \end{itemize} \begin{verbatim} integrate(a^z, z= 0..I*%plusInfinity) integrate((1*z-3)/(2+(0*z-4)^2), z= %minusInfinity..1+I*%plusInfinity) \end{verbatim} \subsection{(279) Risch Algorithm Boundary Cases} \begin{itemize} \item (3) PFO::possibleOrder: more than 1 algebraic constant \end{itemize} \begin{verbatim} integrate(tan(z)/sqrt(sin(z+%pi/4)), z= 0..1,"noPole") \end{verbatim} \begin{itemize} \item (1) Not integrable (provided residues have no relations) \end{itemize} \begin{verbatim} integrate(((z^3-1)/(1+z))^(1/2)/z^2, z= 1..%plusInfinity,"noPole") \end{verbatim} \begin{itemize} \item (35) integrate: implementation incomplete (non-algebraic residues) \end{itemize} \begin{verbatim} integrate(-(1-(I*z)^(1/2)/(1-I*z))^(1/2), z= -1..1,"noPole") \end{verbatim} \begin{itemize} \item (177) integrate: implementation incomplete (constant residues) \end{itemize} \begin{verbatim} integrate(sin(z)^2*(1+z^(1/2))^(1/2), z= 0..1,"noPole") \end{verbatim} \begin{itemize} \item (22) Imaginary part is nonzero. Cannot retract. \end{itemize} \begin{verbatim} integrate(sqrt(sin(2*z))/sqrt(cos(2*z)),z) \end{verbatim} \begin{itemize} \item (29) Function not supported by Risch d.e. \end{itemize} \begin{verbatim} integrate(exp(-I*(I*z)^(1/2))/abs(z)^2, z= 0..1,"noPole") \end{verbatim} \begin{itemize} \item (12) integrate: implementation incomplete (residue poly has multiple non-linear factors) \end{itemize} \begin{verbatim} integrate(tanh(z)^(4/3), z = -1..1,"noPole") \end{verbatim} \begin{itemize} \item (0) integralBasis: possible wild ramification \end{itemize} \subsection{(2331) Failed Results} \begin{itemize} \item (2033) "failed" \end{itemize} \begin{verbatim} integrate(log(2-z^2)/(1-z^3), z= 0..1) \end{verbatim} \begin{itemize} \item (56) Sorry - cannot handle that integrand yet \end{itemize} \begin{verbatim} integrate(erf((I*z)^(1/3)), z= -1..1,"noPole") \end{verbatim} \begin{itemize} \item (242) failed - cannot handle that integrand \end{itemize} \begin{verbatim} integrate(sin(1/z)+(1-1/z^4)^(1/2), z= 0..%pi,"noPole") \end{verbatim} \subsection{(490) Successful Results} \subsection{(305) Indeterminate Results} There were some integrals that OpenAxiom failed to complete given the bounds on the allowed CPU time (about 10 minutes of execution). Further effort will be applied to try to resolve these cases. It may be that some portion of the integration algorithm either has an infinite loop or has non-polynomial time behavior. We will attempt to investigate both possibilities. Tim <<*>>= )set mes auto off )set break resume in1012a:=integrate(log(abs(z^3-1))/(1+z)^2, z= 0..%plusInfinity,"noPole") -- +-+ -- %pi\|3 -- (4) ------- -- 3 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in101a:=integrate((sqrt(z)^I)^I, z= 0..1,"noPole") -- 2 -- (2) ------ -- 2 -- I + 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in106a:=integrate(((I+z)^I)^I, z= 0..1,"noPole") -- -- 2 2 -- I log(I + 1) I log(I) -- (I + 1)%e - I %e -- (3) ------------------------------------ -- 2 -- I + 1 -- Type: Union(f1: OrderedCompletion Expression Integer,...) -- in108a:=integrate(sqrt((1 + cos(z))*(1 + sin(z))),z=0..%plusInfinity,"noPole") -- -- + infinity -- in119a:=integrate(log(1/z+sqrt(1+1/z)), z=0..1,"noPole") -- +-+ +-+ +-+ -- 3log(2\|2 + 3) + 2log(\|2 + 1) - 3log(- 2\|2 + 3) -- + -- +-+ +-+ +-+ -- +-+ (- 32\|2 - 30)\|5 + 48\|2 + 102 +-+ -- \|5 log(----------------------------------) - log(4)\|5 -- +-+ -- 2\|2 + 3 -- / -- 4 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in120a:=integrate(1/(1+1/z^6), z=0..%plusInfinity) -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) -- in1029a:=integrate((I*z/(I*z+1))^(1/2), z= 0..%plusInfinity,"noPole") -- -- + infinity in1030a:=integrate(I*z/(I*z+1), z= 0..%plusInfinity,"noPole") -- -- + infinity in1066a:=integrate(acoth(z)*real(z), z= 0..1,"noPole") -- 1 -- (6) - -- 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1067a:=integrate(acoth(z)*z^(1/2), z= 0..1,"noPole") -- - 2log(2) - %pi + 8 -- (8) ------------------- -- 6 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1076a:=integrate(sin(z)*(1-cos(z)/(1-sin(z)^2)^(1/2))^2, z= 0..1,"noPole") -- - 4cos(1) + 4 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1084a:=integrate(atan(sin(z))+atan(1/sin(z)), z= 0..1,"noPole") -- %pi -- - --- -- 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1107a:=integrate(-log(z)/(-1+z^(1/2))^3, z= 0..1/2*I,"noPole") -- -- +-+ -- +-+ +-+ \|I -- ((2I + 12)\|I + (- 6I - 4)\|2 )log(----) -- +-+ -- \|2 -- + -- +-+ +-+ -- +-+ +-+ - 4\|I + (I + 2)\|2 -- ((- I - 6)\|I + (3I + 2)\|2 )log(---------------------) -- +-+ -- 2\|2 -- + -- 2 2 -- I +-+ +-+ I +-+ -- (- 3log(--) + 2I + 4)\|I + (I + 1)\|2 log(--) - 4I\|2 -- 4 4 -- / -- +-+ +-+ -- (I + 6)\|I + (- 3I - 2)\|2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1108a:=integrate(log(z)/(-1+z^(1/2))^3, z= 0..1/2*I,"noPole") -- -- +-+ -- +-+ +-+ \|I -- ((- 2I - 12)\|I + (6I + 4)\|2 )log(----) -- +-+ -- \|2 -- + -- +-+ +-+ -- +-+ +-+ - 4\|I + (I + 2)\|2 -- ((I + 6)\|I + (- 3I - 2)\|2 )log(---------------------) -- +-+ -- 2\|2 -- + -- 2 2 -- I +-+ +-+ I +-+ -- (3log(--) - 2I - 4)\|I + (- I - 1)\|2 log(--) + 4I\|2 -- 4 4 -- / -- +-+ +-+ -- (I + 6)\|I + (- 3I - 2)\|2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1112a:=integrate((1-1/z)^(1/2), z= %pi..2*%pi,"noPole") -- -- +--------+ +-------+ -- |2%pi - 1 |%pi - 1 -- - 2log( |-------- + 1) + 2log( |------- + 1) -- \| 2%pi \| %pi -- + -- +-------+ +--------+ -- |%pi - 1 |2%pi - 1 -- - 2%pi |------- + 2%pi - 1 - 4%pi |-------- + 4%pi - 1 -- \| %pi \| 2%pi -- - log(---------------------------) + log(----------------------------) -- %pi 2%pi -- + -- +--------+ +-------+ -- |2%pi - 1 |%pi - 1 -- 8%pi |-------- - 4%pi |------- -- \| 2%pi \| %pi -- / -- 4 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1114a:=integrate(-z-(1/2*2^(1/2)+1/2*I*2^(1/2))*z^(1/2), z= 1..%plusInfinity,"noPole") -- -- - infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) ------------------------------------------------------ in1118:=integrate(acot(z), z= 0..1/2*I) -- -- 2 -- I + 4 4I -- 2log(------) + I atan(------) -- 4 2 -- I - 4 -- ----------------------------- -- 4 -- Type: Union(f1: OrderedCompletion Expression Integer,...) ------------------------------------------------------ in1120a:=integrate((z^2)^(1/2), z= 1..2,"noPole") -- -- 3 -- (29) - -- 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) ------------------------------------------------------ in1130a:=integrate(3^log(z), z= -%i..%i,"noPole") -- -- -- log(3)log(I) log(3)log(- I) -- I %e + I %e -- (45) ------------------------------------- -- log(3) + 1 -- Type: Union(f1: OrderedCompletion Expression Integer,...) -- ------------------------------------------------------ in1149:=integrate(imag(z)*z^(1/6), z= -%i..%i) -- -- (49) 0 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1149:=integrate(imag(z)*z^(1/6), z= -%i..%i) -- -- (64) 0 -- Type: Union(f1: OrderedCompletion Expression Complex Integer,...) in1150a:=integrate(1/z^(1/2), z= -%i..%i,"noPole") -- -- +-+ +---+ -- (51) 2\|I - 2\|- I -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1150c:=integrate(1/z^(1/2), z= -%i..%i,"noPole") -- -- +--+ +----+ -- (66) 2\|%i - 2\|- %i -- Type: Union(f1: OrderedCompletion Expression Complex Integer,...) in1161:=integrate(hermiteH(1, z), z= -%i..%i) -- -- (76) 0 -- Type: Union(f1: OrderedCompletion Expression Integer,...) -- in1161a:=integrate(hermiteH(1, z), z= -%i..%i) -- -- -- (77) 0 -- Type: Union(f1: OrderedCompletion Expression Complex Integer,...) in1160:=integrate(HermiteH(2, z), z= -%i..%i) -- 20%i -- - ---- -- 3 -- Type: Union(f1: OrderedCompletion Expression Complex Integer,...) in1162:=integrate(laguerreL(1, z), z= -%i..%i) -- -- (78) 2I -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1162:=integrate(laguerreL(1, z), z= -%i..%i) -- -- (79) 2%i -- Type: Union(f1: OrderedCompletion Expression Complex Integer,...) in1163:=integrate(legendreP(3, z), z= -%i..%i) -- -- (80) 0 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1163:=integrate(legendreP(3, z), z= -%i..%i) -- -- (81) 0 -- Type: Union(f1: OrderedCompletion Expression Complex Integer,...) in1164:=integrate(legendreP(2, z), z= -%i..%i) -- -- 3 -- (82) I - I -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1164:=integrate(legendreP(2, z), z= -%i..%i) -- -- (83) - 2%i -- Type: Union(f1: OrderedCompletion Expression Complex Integer,...) -- in1167a:=integrate((z^2)^(1/6), z= -3..-1,"noPole") -- -- 3+---+ 3+---+ -- - 3\|- 1 + 9\|- 3 -- (85) ------------------- -- 4 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1180:=integrate(z^(1/3)/(z^2+1), z= 0..10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) -- -- potentialPole -- in1180:=integrate(z^(1/3)/(z^2+1), z= 0..10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000,"noPole") 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99999999999999999999999999999999999999999999999999999999999999_ -- 99999999999999999999999999999999999999999999999999999999999999_ -- 99999999999999999999999999999999999999999999999999999999999999_ -- 99999999999999999999999999999999999999999999999999999999999999_ -- 99999999999999999999999999999999999999999999999999999999999999_ -- 99999999999999999999999999999999999999999999999999999999999999_ -- 99999999999999999999999999999999999999999999999999999999999999_ -- 99998000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 000000000000000000000000000 -- * -- 3+--+2 -- \|10 -- + -- 300000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000000_ -- 000000000000000000000000000000000000000000000 -- * -- 3+--+ -- \|10 -- + -- - -- 19999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999999999_ -- 9999999999999999999999999999999999999999999999999999999 -- + -- - -- 12 -- * -- log -- 100000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000_ -- 00000000000000000000000000000000000000000000000000000000000_ -- 00000000000 -- * -- 3+--+2 -- \|10 -- + -- 1 -- + -- +-+ -- 12\|3 -- * -- atan -- 2000000000000000000000000000000000000000000000000000000000000_ -- 000000000000000000000000000000000000000000000000000000000000_ -- 000000000000000000000000000000000000000000000000000000000000_ -- 000000000000000000000000000000000000000000000000000000000000_ -- 000000000000000000000000000000000000000000000000000000000000_ -- 000000000000000000000000000000000000000000000000000000000000_ -- 000000000000000000000000000000000000000000000000000000000000_ -- 000000000000000000000000000000000000000000000000000000000000_ -- 000000000000000000000000000000000000000000000000000000000000_ -- 000000000000000000000000000000000000000000000000000000000000_ -- 000000000000000000000000000000000000000000000000000000000000_ -- 000000000000000000000000000000000000000000000000000000000000_ -- 000000000000000000000000000000000000000000000000000000000000_ -- 000000000000000000000000000000000000000000000000000000000000_ -- 000000000000000000000000000000000000000000000000000000000000_ -- 000000000000000000000000000000000000000000000000000000000000_ -- 000000000000000000000000000000000000000000000000000000 -- * -- 3+--+2 -- \|10 -- + -- - 1 -- / -- +-+ -- \|3 -- + -- +-+ -- 2%pi\|3 -- / -- 24 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1183a:=integrate(csc(z), z= 1-%i..1+%i,"noPole") -- -- 2 2 -- sin(I + 1) sin(I - 1) -- log(-----------------------------) - log(-----------------------------) -- 2 2 -- cos(I + 1) + 2cos(I + 1) + 1 cos(I - 1) + 2cos(I - 1) + 1 -- ----------------------------------------------------------------------- -- 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1185a:=integrate((z+1)^(1/2)/(1+z^4), z= 0..1,"noPole") -- -- ROOT -- +-----------------------------------------+ -- | 2 2 +-+ -- \|- 96%%CZ1 - 64%%CZ0 %%CZ1 - 96%%CZ0 - 1 - 4\|2 %%CZ1 -- + -- +-+ -- - 4\|2 %%CZ0 -- / -- +-+ -- 2\|2 -- * -- log -- +-+ +-+ +-+ +-+ -- ((24576\|2 %%CZ0 - 768\|2 )%%CZ1 - 768\|2 %%CZ0 - 48\|2 ) -- * -- +-----------------------------------------+ -- | 2 2 -- \|- 96%%CZ1 - 64%%CZ0 %%CZ1 - 96%%CZ0 - 1 -- + -- 2 2 -- (196608%%CZ0 - 6144)%%CZ1 + (196608%%CZ0 + 384)%%CZ1 -- + -- 2 -- - 6144%%CZ0 + 384%%CZ0 + 48 -- * -- ROOT -- +-----------------------------------------+ -- | 2 2 -- \|- 96%%CZ1 - 64%%CZ0 %%CZ1 - 96%%CZ0 - 1 -- + -- +-+ +-+ -- - 4\|2 %%CZ1 - 4\|2 %%CZ0 -- / -- +-+ -- 2\|2 -- + -- ((- 3072%%CZ0 + 384)%%CZ1 + 384%%CZ0 - 12) -- * -- +-----------------------------------------+ -- | 2 2 -- \|- 96%%CZ1 - 64%%CZ0 %%CZ1 - 96%%CZ0 - 1 -- + -- +-+ +-+ 2 -- (- 12288\|2 %%CZ0 + 1536\|2 )%%CZ1 -- + -- +-+ 2 +-+ +-+ 2 +-+ -- (- 12288\|2 %%CZ0 + 48\|2 )%%CZ1 + 1536\|2 %%CZ0 + 48\|2 %%CZ0 -- + -- +-+ -- 60\|2 -- / -- +-+ -- \|2 -- + -- - -- ROOT -- +-----------------------------------------+ -- | 2 2 +-+ -- \|- 96%%CZ1 - 64%%CZ0 %%CZ1 - 96%%CZ0 - 1 - 4\|2 %%CZ1 -- + -- +-+ -- - 4\|2 %%CZ0 -- / -- +-+ -- 2\|2 -- * -- log -- ((24576%%CZ0 - 768)%%CZ1 - 768%%CZ0 - 48) -- * -- +-----------------------------------------+ -- | 2 2 -- \|- 96%%CZ1 - 64%%CZ0 %%CZ1 - 96%%CZ0 - 1 -- + -- +-+ +-+ 2 -- (98304\|2 %%CZ0 - 3072\|2 )%%CZ1 -- + -- +-+ 2 +-+ +-+ 2 -- (98304\|2 %%CZ0 + 192\|2 )%%CZ1 - 3072\|2 %%CZ0 -- + -- +-+ +-+ -- 192\|2 %%CZ0 + 24\|2 -- * -- ROOT -- +-----------------------------------------+ -- | 2 2 -- \|- 96%%CZ1 - 64%%CZ0 %%CZ1 - 96%%CZ0 - 1 -- + -- +-+ +-+ -- - 4\|2 %%CZ1 - 4\|2 %%CZ0 -- / -- +-+ -- 2\|2 -- + -- ((- 3072%%CZ0 + 384)%%CZ1 + 384%%CZ0 - 12) -- * -- +-----------------------------------------+ -- | 2 2 -- \|- 96%%CZ1 - 64%%CZ0 %%CZ1 - 96%%CZ0 - 1 -- + -- +-+ +-+ 2 -- (- 12288\|2 %%CZ0 + 1536\|2 )%%CZ1 -- + -- +-+ 2 +-+ +-+ 2 -- (- 12288\|2 %%CZ0 + 48\|2 )%%CZ1 + 1536\|2 %%CZ0 -- + -- +-+ +-+ -- 48\|2 %%CZ0 + 42\|2 -- / -- +-+ -- \|2 -- + -- - -- ROOT -- +-----------------------------------------+ -- | 2 2 +-+ -- - \|- 96%%CZ1 - 64%%CZ0 %%CZ1 - 96%%CZ0 - 1 - 4\|2 %%CZ1 -- + -- +-+ -- - 4\|2 %%CZ0 -- / -- +-+ -- 2\|2 -- * -- log -- +-+ +-+ +-+ -- (24576\|2 %%CZ0 - 768\|2 )%%CZ1 - 768\|2 %%CZ0 -- + -- +-+ -- - 48\|2 -- * -- +-----------------------------------------+ -- | 2 2 -- \|- 96%%CZ1 - 64%%CZ0 %%CZ1 - 96%%CZ0 - 1 -- + -- 2 -- (- 196608%%CZ0 + 6144)%%CZ1 -- + -- 2 2 -- (- 196608%%CZ0 - 384)%%CZ1 + 6144%%CZ0 - 384%%CZ0 - 48 -- * -- ROOT -- +-----------------------------------------+ -- | 2 2 -- - \|- 96%%CZ1 - 64%%CZ0 %%CZ1 - 96%%CZ0 - 1 -- + -- +-+ +-+ -- - 4\|2 %%CZ1 - 4\|2 %%CZ0 -- / -- +-+ -- 2\|2 -- + -- ((3072%%CZ0 - 384)%%CZ1 - 384%%CZ0 + 12) -- * -- +-----------------------------------------+ -- | 2 2 -- \|- 96%%CZ1 - 64%%CZ0 %%CZ1 - 96%%CZ0 - 1 -- + -- +-+ +-+ 2 -- (- 12288\|2 %%CZ0 + 1536\|2 )%%CZ1 -- + -- +-+ 2 +-+ +-+ 2 -- (- 12288\|2 %%CZ0 + 48\|2 )%%CZ1 + 1536\|2 %%CZ0 -- + -- +-+ +-+ -- 48\|2 %%CZ0 + 60\|2 -- / -- +-+ -- \|2 -- + -- ROOT -- +-----------------------------------------+ -- | 2 2 +-+ -- - \|- 96%%CZ1 - 64%%CZ0 %%CZ1 - 96%%CZ0 - 1 - 4\|2 %%CZ1 -- + -- +-+ -- - 4\|2 %%CZ0 -- / -- +-+ -- 2\|2 -- * -- log -- ((24576%%CZ0 - 768)%%CZ1 - 768%%CZ0 - 48) -- * -- +-----------------------------------------+ -- | 2 2 -- \|- 96%%CZ1 - 64%%CZ0 %%CZ1 - 96%%CZ0 - 1 -- + -- +-+ +-+ 2 -- (- 98304\|2 %%CZ0 + 3072\|2 )%%CZ1 -- + -- +-+ 2 +-+ +-+ 2 -- (- 98304\|2 %%CZ0 - 192\|2 )%%CZ1 + 3072\|2 %%CZ0 -- + -- +-+ +-+ -- - 192\|2 %%CZ0 - 24\|2 -- * -- ROOT -- +-----------------------------------------+ -- | 2 2 -- - \|- 96%%CZ1 - 64%%CZ0 %%CZ1 - 96%%CZ0 - 1 -- + -- +-+ +-+ -- - 4\|2 %%CZ1 - 4\|2 %%CZ0 -- / -- +-+ -- 2\|2 -- + -- ((3072%%CZ0 - 384)%%CZ1 - 384%%CZ0 + 12) -- * -- +-----------------------------------------+ -- | 2 2 -- \|- 96%%CZ1 - 64%%CZ0 %%CZ1 - 96%%CZ0 - 1 -- + -- +-+ +-+ 2 -- (- 12288\|2 %%CZ0 + 1536\|2 )%%CZ1 -- + -- +-+ 2 +-+ +-+ 2 +-+ -- (- 12288\|2 %%CZ0 + 48\|2 )%%CZ1 + 1536\|2 %%CZ0 + 48\|2 %%CZ0 -- + -- +-+ -- 42\|2 -- / -- +-+ -- \|2 -- + -- - -- ROOT -- +-----------------------------------------+ -- | 2 2 +-+ -- - \|- 96%%CZ1 - 64%%CZ0 %%CZ1 - 96%%CZ0 - 1 - 4\|2 %%CZ1 -- + -- +-+ -- - 4\|2 %%CZ0 -- / -- +-+ -- 2\|2 -- * -- log -- ((- 24576%%CZ0 + 768)%%CZ1 + 768%%CZ0 + 48) -- * -- +-----------------------------------------+ -- | 2 2 -- \|- 96%%CZ1 - 64%%CZ0 %%CZ1 - 96%%CZ0 - 1 -- + -- +-+ +-+ 2 -- (98304\|2 %%CZ0 - 3072\|2 )%%CZ1 -- + -- +-+ 2 +-+ +-+ 2 -- (98304\|2 %%CZ0 + 192\|2 )%%CZ1 - 3072\|2 %%CZ0 -- + -- +-+ +-+ -- 192\|2 %%CZ0 + 24\|2 -- * -- ROOT -- +-----------------------------------------+ -- | 2 2 -- - \|- 96%%CZ1 - 64%%CZ0 %%CZ1 - 96%%CZ0 - 1 -- + -- +-+ +-+ -- - 4\|2 %%CZ1 - 4\|2 %%CZ0 -- / -- +-+ -- 2\|2 -- + -- ((3072%%CZ0 - 384)%%CZ1 - 384%%CZ0 + 12) -- * -- +-----------------------------------------+ -- | 2 2 -- \|- 96%%CZ1 - 64%%CZ0 %%CZ1 - 96%%CZ0 - 1 -- + -- +-+ +-+ 2 -- (- 12288\|2 %%CZ0 + 1536\|2 )%%CZ1 -- + -- +-+ 2 +-+ +-+ 2 -- (- 12288\|2 %%CZ0 + 48\|2 )%%CZ1 + 1536\|2 %%CZ0 -- + -- +-+ +-+ -- 48\|2 %%CZ0 + 42\|2 -- / -- +-+ -- \|2 -- + -- ROOT -- +-----------------------------------------+ -- | 2 2 +-+ -- - \|- 96%%CZ1 - 64%%CZ0 %%CZ1 - 96%%CZ0 - 1 - 4\|2 %%CZ1 -- + -- +-+ -- - 4\|2 %%CZ0 -- / -- +-+ -- 2\|2 -- * -- log -- +-+ +-+ +-+ -- (- 24576\|2 %%CZ0 + 768\|2 )%%CZ1 + 768\|2 %%CZ0 -- + -- +-+ -- 48\|2 -- * -- +-----------------------------------------+ -- | 2 2 -- \|- 96%%CZ1 - 64%%CZ0 %%CZ1 - 96%%CZ0 - 1 -- + -- 2 2 -- (196608%%CZ0 - 6144)%%CZ1 + (196608%%CZ0 + 384)%%CZ1 -- + -- 2 -- - 6144%%CZ0 + 384%%CZ0 + 48 -- * -- ROOT -- +-----------------------------------------+ -- | 2 2 -- - \|- 96%%CZ1 - 64%%CZ0 %%CZ1 - 96%%CZ0 - 1 -- + -- +-+ +-+ -- - 4\|2 %%CZ1 - 4\|2 %%CZ0 -- / -- +-+ -- 2\|2 -- + -- ((3072%%CZ0 - 384)%%CZ1 - 384%%CZ0 + 12) -- * -- +-----------------------------------------+ -- | 2 2 -- \|- 96%%CZ1 - 64%%CZ0 %%CZ1 - 96%%CZ0 - 1 -- + -- +-+ +-+ 2 -- (- 12288\|2 %%CZ0 + 1536\|2 )%%CZ1 -- + -- +-+ 2 +-+ +-+ 2 +-+ -- (- 12288\|2 %%CZ0 + 48\|2 )%%CZ1 + 1536\|2 %%CZ0 + 48\|2 %%CZ0 -- + -- +-+ -- 60\|2 -- / -- +-+ -- \|2 -- + -- ROOT -- +-----------------------------------------+ -- | 2 2 +-+ -- \|- 96%%CZ1 - 64%%CZ0 %%CZ1 - 96%%CZ0 - 1 - 4\|2 %%CZ1 -- + -- +-+ -- - 4\|2 %%CZ0 -- / -- +-+ -- 2\|2 -- * -- log -- ((- 24576%%CZ0 + 768)%%CZ1 + 768%%CZ0 + 48) -- * -- +-----------------------------------------+ -- | 2 2 -- \|- 96%%CZ1 - 64%%CZ0 %%CZ1 - 96%%CZ0 - 1 -- + -- +-+ +-+ 2 -- (- 98304\|2 %%CZ0 + 3072\|2 )%%CZ1 -- + -- +-+ 2 +-+ +-+ 2 -- (- 98304\|2 %%CZ0 - 192\|2 )%%CZ1 + 3072\|2 %%CZ0 -- + -- +-+ +-+ -- - 192\|2 %%CZ0 - 24\|2 -- * -- ROOT -- +-----------------------------------------+ -- | 2 2 -- \|- 96%%CZ1 - 64%%CZ0 %%CZ1 - 96%%CZ0 - 1 -- + -- +-+ +-+ -- - 4\|2 %%CZ1 - 4\|2 %%CZ0 -- / -- +-+ -- 2\|2 -- + -- ((- 3072%%CZ0 + 384)%%CZ1 + 384%%CZ0 - 12) -- * -- +-----------------------------------------+ -- | 2 2 -- \|- 96%%CZ1 - 64%%CZ0 %%CZ1 - 96%%CZ0 - 1 -- + -- +-+ +-+ 2 -- (- 12288\|2 %%CZ0 + 1536\|2 )%%CZ1 -- + -- +-+ 2 +-+ +-+ 2 +-+ -- (- 12288\|2 %%CZ0 + 48\|2 )%%CZ1 + 1536\|2 %%CZ0 + 48\|2 %%CZ0 -- + -- +-+ -- 42\|2 -- / -- +-+ -- \|2 -- + -- - -- ROOT -- +-----------------------------------------+ -- | 2 2 +-+ -- \|- 96%%CZ1 - 64%%CZ0 %%CZ1 - 96%%CZ0 - 1 - 4\|2 %%CZ1 -- + -- +-+ -- - 4\|2 %%CZ0 -- / -- +-+ -- 2\|2 -- * -- log -- +-+ +-+ +-+ -- (- 24576\|2 %%CZ0 + 768\|2 )%%CZ1 + 768\|2 %%CZ0 -- + -- +-+ -- 48\|2 -- * -- +-----------------------------------------+ -- | 2 2 -- \|- 96%%CZ1 - 64%%CZ0 %%CZ1 - 96%%CZ0 - 1 -- + -- 2 -- (- 196608%%CZ0 + 6144)%%CZ1 -- + -- 2 2 -- (- 196608%%CZ0 - 384)%%CZ1 + 6144%%CZ0 - 384%%CZ0 - 48 -- * -- ROOT -- +-----------------------------------------+ -- | 2 2 -- \|- 96%%CZ1 - 64%%CZ0 %%CZ1 - 96%%CZ0 - 1 -- + -- +-+ +-+ -- - 4\|2 %%CZ1 - 4\|2 %%CZ0 -- / -- +-+ -- 2\|2 -- + -- ((- 3072%%CZ0 + 384)%%CZ1 + 384%%CZ0 - 12) -- * -- +-----------------------------------------+ -- | 2 2 -- \|- 96%%CZ1 - 64%%CZ0 %%CZ1 - 96%%CZ0 - 1 -- + -- +-+ +-+ 2 -- (- 12288\|2 %%CZ0 + 1536\|2 )%%CZ1 -- + -- +-+ 2 +-+ +-+ 2 -- (- 12288\|2 %%CZ0 + 48\|2 )%%CZ1 + 1536\|2 %%CZ0 -- + -- +-+ +-+ -- 48\|2 %%CZ0 + 60\|2 -- / -- +-+ -- \|2 -- + -- - -- +------+ -- \|4%%CZ1 -- * -- log -- +-+ +-+ 2 -- (98304\|2 %%CZ0 - 3072\|2 )%%CZ1 -- + -- +-+ 2 +-+ +-+ 3 -- (98304\|2 %%CZ0 + 192\|2 )%%CZ1 + 98304\|2 %%CZ0 -- + -- +-+ +-+ -- 768\|2 %%CZ0 - 36\|2 -- * -- +------+ -- \|4%%CZ1 -- + -- 2 2 -- (12288%%CZ0 - 1536)%%CZ1 + (12288%%CZ0 - 48)%%CZ1 -- + -- 3 -- 12288%%CZ0 + 96%%CZ0 + 18 -- + -- +------+ -- \|4%%CZ1 -- * -- log -- 2 2 -- (98304%%CZ0 - 3072)%%CZ1 + (98304%%CZ0 + 192)%%CZ1 -- + -- 3 -- 98304%%CZ0 + 768%%CZ0 - 36 -- * -- +------+ -- \|4%%CZ1 -- + -- 2 2 3 -- (12288%%CZ0 - 1536)%%CZ1 + (12288%%CZ0 - 48)%%CZ1 + 12288%%CZ0 -- + -- 96%%CZ0 + 9 -- + -- - -- +------+ -- \|4%%CZ1 -- * -- log -- 2 2 -- (- 98304%%CZ0 + 3072)%%CZ1 + (- 98304%%CZ0 - 192)%%CZ1 -- + -- 3 -- - 98304%%CZ0 - 768%%CZ0 + 36 -- * -- +------+ -- \|4%%CZ1 -- + -- 2 2 -- (12288%%CZ0 - 1536)%%CZ1 + (12288%%CZ0 - 48)%%CZ1 -- + -- 3 -- 12288%%CZ0 + 96%%CZ0 + 9 -- + -- +------+ -- \|4%%CZ1 -- * -- log -- +-+ +-+ 2 -- (- 98304\|2 %%CZ0 + 3072\|2 )%%CZ1 -- + -- +-+ 2 +-+ +-+ 3 -- (- 98304\|2 %%CZ0 - 192\|2 )%%CZ1 - 98304\|2 %%CZ0 -- + -- +-+ +-+ -- - 768\|2 %%CZ0 + 36\|2 -- * -- +------+ -- \|4%%CZ1 -- + -- 2 2 3 -- (12288%%CZ0 - 1536)%%CZ1 + (12288%%CZ0 - 48)%%CZ1 + 12288%%CZ0 -- + -- 96%%CZ0 + 18 -- + -- +------+ -- \|4%%CZ0 -- * -- log -- +-+ 3 +-+ 2 +-+ +-+ -- (98304\|2 %%CZ0 + 3072\|2 %%CZ0 + 576\|2 %%CZ0 - 60\|2 ) -- * -- +------+ -- \|4%%CZ0 -- + -- 3 2 -- - 12288%%CZ0 - 1536%%CZ0 - 144%%CZ0 + 30 -- + -- - -- +------+ -- \|4%%CZ0 -- * -- log -- 3 2 +------+ -- (98304%%CZ0 + 3072%%CZ0 + 576%%CZ0 - 60)\|4%%CZ0 -- + -- 3 2 -- - 12288%%CZ0 - 1536%%CZ0 - 144%%CZ0 + 21 -- + -- +------+ -- \|4%%CZ0 -- * -- log -- 3 2 +------+ -- (- 98304%%CZ0 - 3072%%CZ0 - 576%%CZ0 + 60)\|4%%CZ0 -- + -- 3 2 -- - 12288%%CZ0 - 1536%%CZ0 - 144%%CZ0 + 21 -- + -- - -- +------+ -- \|4%%CZ0 -- * -- log -- +-+ 3 +-+ 2 +-+ +-+ -- (- 98304\|2 %%CZ0 - 3072\|2 %%CZ0 - 576\|2 %%CZ0 + 60\|2 ) -- * -- +------+ -- \|4%%CZ0 -- + -- 3 2 -- - 12288%%CZ0 - 1536%%CZ0 - 144%%CZ0 + 30 -- / -- 4 -- Type: Union(f1: OrderedCompletion Expression Integer,...) -- -- in1186a:=integrate((z^2+z)^(1/2)/(1+z^2)^2, z= 0..1,"noPole") -- -- (105) -- +-+ 4+-+ %pi -- (17\|2 - 24)\|2 cos(---) -- 8 -- * -- log -- %pi 4 +-+4+-+3 %pi 3 -- 2sin(---) + 2\|2 \|2 sin(---) -- 8 8 -- + -- %pi 2 +-+4+-+3 %pi 4+-+2 %pi 2 -- (4cos(---) - 2\|2 \|2 cos(---) + 4\|2 )sin(---) -- 8 8 8 -- + -- +-+4+-+3 %pi 2 4+-+2 %pi +-+4+-+ %pi -- (2\|2 \|2 cos(---) - 4\|2 cos(---) + 2\|2 \|2 )sin(---) -- 8 8 8 -- + -- %pi 4 +-+4+-+3 %pi 3 4+-+2 %pi 2 -- 2cos(---) - 2\|2 \|2 cos(---) + 4\|2 cos(---) -- 8 8 8 -- + -- +-+4+-+ %pi -- - 2\|2 \|2 cos(---) + 1 -- 8 -- + -- +-+ 4+-+ %pi -- (- 17\|2 + 24)\|2 cos(---) -- 8 -- * -- log -- %pi 4 4+-+3 %pi 3 -- 2sin(---) + 4\|2 sin(---) -- 8 8 -- + -- %pi 2 +-+ 4+-+3 %pi +-+ 4+-+2 -- (4cos(---) + (- 4\|2 + 4)\|2 cos(---) + (- 4\|2 + 12)\|2 ) -- 8 8 -- * -- %pi 2 -- sin(---) -- 8 -- + -- 4+-+3 %pi 2 +-+ 4+-+2 %pi -- 4\|2 cos(---) + (- 8\|2 + 8)\|2 cos(---) -- 8 8 -- + -- +-+ 4+-+ -- (- 8\|2 + 16)\|2 -- * -- %pi -- sin(---) -- 8 -- + -- %pi 4 +-+ 4+-+3 %pi 3 -- 2cos(---) + (- 4\|2 + 4)\|2 cos(---) -- 8 8 -- + -- +-+ 4+-+2 %pi 2 +-+ 4+-+ %pi -- (- 12\|2 + 20)\|2 cos(---) + (- 24\|2 + 32)\|2 cos(---) -- 8 8 -- + -- +-+ -- - 16\|2 + 24 -- + -- +-+ 4+-+ %pi -- (17\|2 - 24)\|2 cos(---) -- 8 -- * -- log -- %pi 4 4+-+3 %pi 3 -- 2sin(---) - 4\|2 sin(---) -- 8 8 -- + -- %pi 2 +-+ 4+-+3 %pi +-+ 4+-+2 -- (4cos(---) + (4\|2 - 4)\|2 cos(---) + (- 4\|2 + 12)\|2 ) -- 8 8 -- * -- %pi 2 -- sin(---) -- 8 -- + -- 4+-+3 %pi 2 +-+ 4+-+2 %pi -- - 4\|2 cos(---) + (- 8\|2 + 8)\|2 cos(---) -- 8 8 -- + -- +-+ 4+-+ -- (8\|2 - 16)\|2 -- * -- %pi -- sin(---) -- 8 -- + -- %pi 4 +-+ 4+-+3 %pi 3 -- 2cos(---) + (4\|2 - 4)\|2 cos(---) -- 8 8 -- + -- +-+ 4+-+2 %pi 2 +-+ 4+-+ %pi +-+ -- (- 12\|2 + 20)\|2 cos(---) + (24\|2 - 32)\|2 cos(---) - 16\|2 -- 8 8 -- + -- 24 -- + -- +-+ 4+-+ %pi -- (- 17\|2 + 24)\|2 cos(---) -- 8 -- * -- log -- %pi 4 +-+4+-+3 %pi 3 -- 2sin(---) - 2\|2 \|2 sin(---) -- 8 8 -- + -- %pi 2 +-+4+-+3 %pi 4+-+2 %pi 2 -- (4cos(---) + 2\|2 \|2 cos(---) + 4\|2 )sin(---) -- 8 8 8 -- + -- +-+4+-+3 %pi 2 4+-+2 %pi +-+4+-+ %pi -- (- 2\|2 \|2 cos(---) - 4\|2 cos(---) - 2\|2 \|2 )sin(---) -- 8 8 8 -- + -- %pi 4 +-+4+-+3 %pi 3 4+-+2 %pi 2 -- 2cos(---) + 2\|2 \|2 cos(---) + 4\|2 cos(---) -- 8 8 8 -- + -- +-+4+-+ %pi -- 2\|2 \|2 cos(---) + 1 -- 8 -- + -- 4+-+ %pi 4+-+ %pi +-+ -- \|2 sin(---) - \|2 cos(---) + \|2 -- +-+ 4+-+ %pi 8 8 -- (68\|2 - 96)\|2 sin(---)atan(--------------------------------------) -- 8 4+-+ %pi 4+-+ %pi +-+ -- \|2 sin(---) + \|2 cos(---) - \|2 + 2 -- 8 8 -- + -- 4+-+ %pi 4+-+ %pi +-+ -- \|2 sin(---) - \|2 cos(---) + \|2 -- +-+ 4+-+ %pi 8 8 -- (- 68\|2 + 96)\|2 sin(---)atan(----------------------------------) -- 8 4+-+ %pi 4+-+ %pi -- \|2 sin(---) + \|2 cos(---) -- 8 8 -- + -- 4+-+ %pi 4+-+ %pi +-+ -- \|2 sin(---) - \|2 cos(---) - \|2 -- +-+ 4+-+ %pi 8 8 -- (68\|2 - 96)\|2 sin(---)atan(----------------------------------) -- 8 4+-+ %pi 4+-+ %pi -- \|2 sin(---) + \|2 cos(---) -- 8 8 -- + -- 4+-+ %pi 4+-+ %pi +-+ -- \|2 sin(---) - \|2 cos(---) - \|2 -- +-+ 4+-+ %pi 8 8 -- (- 68\|2 + 96)\|2 sin(---)atan(--------------------------------------) -- 8 4+-+ %pi 4+-+ %pi +-+ -- \|2 sin(---) + \|2 cos(---) + \|2 - 2 -- 8 8 -- + -- +-+ -- - 136\|2 + 192 -- / -- +-+ -- 384\|2 - 544 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1190a:=integrate(sin(z)^2*tan(z)^(1/2), z= 0..1,"noPole") -- -- +------+ -- 3 4 2 |sin(1) -- ((96cos(1) + 24cos(1))sin(1) - 96cos(1) + 120cos(1) ) |------ -- \|cos(1) -- + -- 4 2 +-+ -- (- 48cos(1)sin(1) + 96cos(1) - 96cos(1) - 3)\|2 -- * -- log -- 2 2 3 2 -- (- 16cos(1) sin(1) + (- 16cos(1) - 4cos(1))sin(1) - 4cos(1) ) -- * -- +------+ -- +-+ |sin(1) -- \|2 |------ -- \|cos(1) -- + -- 3 2 2 3 -- 8cos(1)sin(1) + 32cos(1) sin(1) + (8cos(1) + 8cos(1))sin(1) + 1 -- + -- +------+ -- 3 4 2 |sin(1) -- ((96cos(1) + 24cos(1))sin(1) - 96cos(1) + 120cos(1) ) |------ -- \|cos(1) -- + -- 4 2 +-+ -- (- 48cos(1)sin(1) + 96cos(1) - 96cos(1) - 3)\|2 -- * -- log -- 2 2 3 -- - 64cos(1) sin(1) + (- 64cos(1) - 16cos(1))sin(1) -- + -- 2 -- - 16cos(1) -- * -- +------+ -- +-+ |sin(1) -- \|2 |------ -- \|cos(1) -- + -- 3 2 2 3 -- 32cos(1)sin(1) + 128cos(1) sin(1) + (32cos(1) + 32cos(1))sin(1) -- + -- 4 -- + -- +------+ -- 3 4 2 |sin(1) -- ((384cos(1) + 96cos(1))sin(1) - 384cos(1) + 480cos(1) ) |------ -- \|cos(1) -- + -- 4 2 +-+ -- (- 192cos(1)sin(1) + 384cos(1) - 384cos(1) - 12)\|2 -- * -- +------+ -- |sin(1) 2 +-+ -- 2cos(1)sin(1) |------ + (- cos(1)sin(1) + cos(1) - 1)\|2 -- \|cos(1) -- atan(-----------------------------------------------------------) -- +------+ -- 2 |sin(1) 2 +-+ -- 2cos(1) |------ + (- cos(1)sin(1) - cos(1) )\|2 -- \|cos(1) -- + -- +------+ -- 3 4 2 |sin(1) -- ((- 384cos(1) - 96cos(1))sin(1) + 384cos(1) - 480cos(1) ) |------ -- \|cos(1) -- + -- 4 2 +-+ -- (192cos(1)sin(1) - 384cos(1) + 384cos(1) + 12)\|2 -- * -- +------+ -- |sin(1) 2 +-+ -- 4cos(1)sin(1) |------ + (- 2cos(1)sin(1) + 2cos(1) - 1)\|2 -- \|cos(1) -- atan(-------------------------------------------------------------) -- +------+ -- 2 |sin(1) 2 +-+ -- 4cos(1) |------ + (- 2cos(1)sin(1) - 2cos(1) + 1)\|2 -- \|cos(1) -- + -- +------+ -- 3 4 2 |sin(1) -- ((- 384cos(1) - 96cos(1))sin(1) + 384cos(1) - 480cos(1) ) |------ -- \|cos(1) -- + -- 4 2 +-+ -- (192cos(1)sin(1) - 384cos(1) + 384cos(1) + 12)\|2 -- * -- +------+ -- |sin(1) 2 +-+ -- 2cos(1)sin(1) |------ + (- cos(1)sin(1) + cos(1) )\|2 -- \|cos(1) -- atan(-------------------------------------------------------) -- +------+ -- 2 |sin(1) 2 +-+ -- 2cos(1) |------ + (- cos(1)sin(1) - cos(1) + 1)\|2 -- \|cos(1) -- + -- 3 5 -- (- 96cos(1) - 24cos(1))log(4) - 1024cos(1) -- + -- 3 -- (96%pi + 1024)cos(1) + (24%pi + 32)cos(1) -- * -- sin(1) -- + -- 4 2 4 -- (96cos(1) - 120cos(1) )log(4) + (- 96%pi - 512)cos(1) -- + -- 2 -- (120%pi + 512)cos(1) -- * -- +------+ -- |sin(1) -- |------ -- \|cos(1) -- + -- 5 3 -- (48cos(1)log(4) + 512cos(1) - 384cos(1) + (- 48%pi - 128)cos(1)) -- * -- sin(1) -- + -- 4 2 6 -- (- 96cos(1) + 96cos(1) + 3)log(4) - 512cos(1) -- + -- 4 2 -- (96%pi + 1152)cos(1) + (- 96%pi - 640)cos(1) - 3%pi -- * -- +-+ -- \|2 -- / -- 3 4 2 +-+ -- ((1024cos(1) + 256cos(1))sin(1) - 1024cos(1) + 1280cos(1) )\|2 -- * -- +------+ -- |sin(1) -- |------ -- \|cos(1) -- + -- 4 2 -- - 1024cos(1)sin(1) + 2048cos(1) - 2048cos(1) - 64 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1191a:=integrate(sin(z)^2/tan(z)^(1/2), z= 0..1,"noPole") -- -- +------+ -- 3 4 2 |sin(1) -- ((- 32cos(1) - 8cos(1))sin(1) + 32cos(1) - 40cos(1) ) |------ -- \|cos(1) -- + -- 4 2 +-+ -- (16cos(1)sin(1) - 32cos(1) + 32cos(1) + 1)\|2 -- * -- log -- 2 2 3 2 -- (- 16cos(1) sin(1) + (- 16cos(1) - 4cos(1))sin(1) - 4cos(1) ) -- * -- +------+ -- +-+ |sin(1) -- \|2 |------ -- \|cos(1) -- + -- 3 2 2 3 -- 8cos(1)sin(1) + 32cos(1) sin(1) + (8cos(1) + 8cos(1))sin(1) + 1 -- + -- +------+ -- 3 4 2 |sin(1) -- ((- 32cos(1) - 8cos(1))sin(1) + 32cos(1) - 40cos(1) ) |------ -- \|cos(1) -- + -- 4 2 +-+ -- (16cos(1)sin(1) - 32cos(1) + 32cos(1) + 1)\|2 -- * -- log -- 2 2 3 -- - 64cos(1) sin(1) + (- 64cos(1) - 16cos(1))sin(1) -- + -- 2 -- - 16cos(1) -- * -- +------+ -- +-+ |sin(1) -- \|2 |------ -- \|cos(1) -- + -- 3 2 2 3 -- 32cos(1)sin(1) + 128cos(1) sin(1) + (32cos(1) + 32cos(1))sin(1) -- + -- 4 -- + -- +------+ -- 3 4 2 |sin(1) -- ((128cos(1) + 32cos(1))sin(1) - 128cos(1) + 160cos(1) ) |------ -- \|cos(1) -- + -- 4 2 +-+ -- (- 64cos(1)sin(1) + 128cos(1) - 128cos(1) - 4)\|2 -- * -- +------+ -- |sin(1) 2 +-+ -- 2cos(1)sin(1) |------ + (- cos(1)sin(1) + cos(1) - 1)\|2 -- \|cos(1) -- atan(-----------------------------------------------------------) -- +------+ -- 2 |sin(1) 2 +-+ -- 2cos(1) |------ + (- cos(1)sin(1) - cos(1) )\|2 -- \|cos(1) -- + -- +------+ -- 3 4 2 |sin(1) -- ((- 128cos(1) - 32cos(1))sin(1) + 128cos(1) - 160cos(1) ) |------ -- \|cos(1) -- + -- 4 2 +-+ -- (64cos(1)sin(1) - 128cos(1) + 128cos(1) + 4)\|2 -- * -- +------+ -- |sin(1) 2 +-+ -- 4cos(1)sin(1) |------ + (- 2cos(1)sin(1) + 2cos(1) - 1)\|2 -- \|cos(1) -- atan(-------------------------------------------------------------) -- +------+ -- 2 |sin(1) 2 +-+ -- 4cos(1) |------ + (- 2cos(1)sin(1) - 2cos(1) + 1)\|2 -- \|cos(1) -- + -- +------+ -- 3 4 2 |sin(1) -- ((- 128cos(1) - 32cos(1))sin(1) + 128cos(1) - 160cos(1) ) |------ -- \|cos(1) -- + -- 4 2 +-+ -- (64cos(1)sin(1) - 128cos(1) + 128cos(1) + 4)\|2 -- * -- +------+ -- |sin(1) 2 +-+ -- 2cos(1)sin(1) |------ + (- cos(1)sin(1) + cos(1) )\|2 -- \|cos(1) -- atan(-------------------------------------------------------) -- +------+ -- 2 |sin(1) 2 +-+ -- 2cos(1) |------ + (- cos(1)sin(1) - cos(1) + 1)\|2 -- \|cos(1) -- + -- 3 3 -- ((32cos(1) + 8cos(1))log(4) + (32%pi + 512)cos(1) + 8%pi cos(1)) -- * -- sin(1) -- + -- 4 2 6 -- (- 32cos(1) + 40cos(1) )log(4) - 1024cos(1) -- + -- 4 2 -- (- 32%pi + 1024)cos(1) + (40%pi + 32)cos(1) -- * -- +------+ -- |sin(1) -- |------ -- \|cos(1) -- + -- 5 3 -- (- 16cos(1)log(4) + 512cos(1) - 640cos(1) - 16%pi cos(1))sin(1) -- + -- 4 2 6 4 -- (32cos(1) - 32cos(1) - 1)log(4) + 512cos(1) + (32%pi - 384)cos(1) -- + -- 2 -- (- 32%pi - 128)cos(1) - %pi -- * -- +-+ -- \|2 -- / -- 3 4 2 +-+ -- ((1024cos(1) + 256cos(1))sin(1) - 1024cos(1) + 1280cos(1) )\|2 -- * -- +------+ -- |sin(1) -- |------ -- \|cos(1) -- + -- 4 2 -- - 1024cos(1)sin(1) + 2048cos(1) - 2048cos(1) - 64 -- Type: Union(f1: OrderedCompletion Expression Integer,...) -- in1193a:=integrate(-sin(z)^2*cot(z-1), z= 0..1,"noPole") -- -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) ------------------------------------------------------ in1207:=integrate(sin(z)*cos(z)*tan(z)^(1/2), z= 0..1) -- -- potentialPole -- in1207a:=integrate(sin(z)*cos(z)*tan(z)^(1/2), z= 0..1,"noPole") -- -- +------+ -- 3 4 2 |sin(1) -- ((- 32cos(1) - 8cos(1))sin(1) + 32cos(1) - 40cos(1) ) |------ -- \|cos(1) -- + -- 4 2 +-+ -- (16cos(1)sin(1) - 32cos(1) + 32cos(1) + 1)\|2 -- * -- log -- 2 2 3 2 -- (- 16cos(1) sin(1) + (- 16cos(1) - 4cos(1))sin(1) - 4cos(1) ) -- * -- +------+ -- +-+ |sin(1) -- \|2 |------ -- \|cos(1) -- + -- 3 2 2 3 -- 8cos(1)sin(1) + 32cos(1) sin(1) + (8cos(1) + 8cos(1))sin(1) + 1 -- + -- +------+ -- 3 4 2 |sin(1) -- ((- 32cos(1) - 8cos(1))sin(1) + 32cos(1) - 40cos(1) ) |------ -- \|cos(1) -- + -- 4 2 +-+ -- (16cos(1)sin(1) - 32cos(1) + 32cos(1) + 1)\|2 -- * -- log -- 2 2 3 -- - 64cos(1) sin(1) + (- 64cos(1) - 16cos(1))sin(1) -- + -- 2 -- - 16cos(1) -- * -- +------+ -- +-+ |sin(1) -- \|2 |------ -- \|cos(1) -- + -- 3 2 2 3 -- 32cos(1)sin(1) + 128cos(1) sin(1) + (32cos(1) + 32cos(1))sin(1) -- + -- 4 -- + -- +------+ -- 3 4 2 |sin(1) -- ((128cos(1) + 32cos(1))sin(1) - 128cos(1) + 160cos(1) ) |------ -- \|cos(1) -- + -- 4 2 +-+ -- (- 64cos(1)sin(1) + 128cos(1) - 128cos(1) - 4)\|2 -- * -- +------+ -- |sin(1) 2 +-+ -- 2cos(1)sin(1) |------ + (- cos(1)sin(1) + cos(1) - 1)\|2 -- \|cos(1) -- atan(-----------------------------------------------------------) -- +------+ -- 2 |sin(1) 2 +-+ -- 2cos(1) |------ + (- cos(1)sin(1) - cos(1) )\|2 -- \|cos(1) -- + -- +------+ -- 3 4 2 |sin(1) -- ((- 128cos(1) - 32cos(1))sin(1) + 128cos(1) - 160cos(1) ) |------ -- \|cos(1) -- + -- 4 2 +-+ -- (64cos(1)sin(1) - 128cos(1) + 128cos(1) + 4)\|2 -- * -- +------+ -- |sin(1) 2 +-+ -- 4cos(1)sin(1) |------ + (- 2cos(1)sin(1) + 2cos(1) - 1)\|2 -- \|cos(1) -- atan(-------------------------------------------------------------) -- +------+ -- 2 |sin(1) 2 +-+ -- 4cos(1) |------ + (- 2cos(1)sin(1) - 2cos(1) + 1)\|2 -- \|cos(1) -- + -- +------+ -- 3 4 2 |sin(1) -- ((- 128cos(1) - 32cos(1))sin(1) + 128cos(1) - 160cos(1) ) |------ -- \|cos(1) -- + -- 4 2 +-+ -- (64cos(1)sin(1) - 128cos(1) + 128cos(1) + 4)\|2 -- * -- +------+ -- |sin(1) 2 +-+ -- 2cos(1)sin(1) |------ + (- cos(1)sin(1) + cos(1) )\|2 -- \|cos(1) -- atan(-------------------------------------------------------) -- +------+ -- 2 |sin(1) 2 +-+ -- 2cos(1) |------ + (- cos(1)sin(1) - cos(1) + 1)\|2 -- \|cos(1) -- + -- 3 3 -- ((32cos(1) + 8cos(1))log(4) + (32%pi + 512)cos(1) + 8%pi cos(1)) -- * -- sin(1) -- + -- 4 2 6 -- (- 32cos(1) + 40cos(1) )log(4) - 1024cos(1) -- + -- 4 2 -- (- 32%pi + 1024)cos(1) + (40%pi + 32)cos(1) -- * -- +------+ -- |sin(1) -- |------ -- \|cos(1) -- + -- 5 3 -- (- 16cos(1)log(4) + 512cos(1) - 640cos(1) - 16%pi cos(1))sin(1) -- + -- 4 2 6 4 -- (32cos(1) - 32cos(1) - 1)log(4) + 512cos(1) + (32%pi - 384)cos(1) -- + -- 2 -- (- 32%pi - 128)cos(1) - %pi -- * -- +-+ -- \|2 -- / -- 3 4 2 +-+ -- ((1024cos(1) + 256cos(1))sin(1) - 1024cos(1) + 1280cos(1) )\|2 -- * -- +------+ -- |sin(1) -- |------ -- \|cos(1) -- + -- 4 2 -- - 1024cos(1)sin(1) + 2048cos(1) - 2048cos(1) - 64 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1210a:=integrate(-sin(z)*cos(z)*cot(z-1), z= 0..1,"noPole") -- -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1214a:=integrate(-sin(z)*tan(z)*csc(z-1), z= 0..1,"noPole") -- -- 1 2 1 2 -- 4cos(-) sin(-) -- 2 2 -- * -- log -- 1 4 1 2 1 2 1 4 2 -- (sin(-) - 2cos(-) sin(-) + cos(-) )sin(1) -- 2 2 2 2 -- + -- 1 1 3 1 3 1 -- (4cos(-)cos(1)sin(-) - 4cos(-) cos(1)sin(-))sin(1) -- 2 2 2 2 -- + -- 1 2 2 1 2 -- 4cos(-) cos(1) sin(-) -- 2 2 -- / -- 1 4 2 1 4 1 4 -- cos(-) cos(1) + 2cos(-) cos(1) + cos(-) -- 2 2 2 -- + -- 1 2 -- sin(-) -- 1 2 1 2 2 -- - 4cos(-) sin(-) log(-------) -- 2 2 1 2 -- cos(-) -- 2 -- + -- 2 -- 1 4 1 2 1 2 1 4 4cos(1) -- (- sin(-) - 2cos(-) sin(-) - cos(-) )log(---------------------) -- 2 2 2 2 2 -- cos(1) + 2cos(1) + 1 -- + -- 1 4 1 2 1 2 1 4 4 -- (sin(-) - 2cos(-) sin(-) + cos(-) )log(---------------------) -- 2 2 2 2 2 -- cos(1) + 2cos(1) + 1 -- + -- 1 1 3 1 3 1 -- - 4cos(-)sin(-) + 4cos(-) sin(-) -- 2 2 2 2 -- / -- 1 4 1 4 -- 2sin(-) - 2cos(-) -- 2 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1217a:=integrate(sin(z)*sec(z)*tan(z)^(1/2), z= 0..1,"noPole") -- -- +------+ -- |sin(1) +-+ -- (2cos(1) |------ + (- sin(1) - cos(1))\|2 ) -- \|cos(1) -- * -- log -- 2 2 3 2 -- (- 16cos(1) sin(1) + (- 16cos(1) - 4cos(1))sin(1) - 4cos(1) ) -- * -- +------+ -- +-+ |sin(1) -- \|2 |------ -- \|cos(1) -- + -- 3 2 2 3 -- 8cos(1)sin(1) + 32cos(1) sin(1) + (8cos(1) + 8cos(1))sin(1) + 1 -- + -- +------+ -- |sin(1) +-+ -- (2cos(1) |------ + (- sin(1) - cos(1))\|2 ) -- \|cos(1) -- * -- log -- 2 2 3 -- - 64cos(1) sin(1) + (- 64cos(1) - 16cos(1))sin(1) -- + -- 2 -- - 16cos(1) -- * -- +------+ -- +-+ |sin(1) -- \|2 |------ -- \|cos(1) -- + -- 3 2 2 3 -- 32cos(1)sin(1) + 128cos(1) sin(1) + (32cos(1) + 32cos(1))sin(1) -- + -- 4 -- + -- +------+ -- |sin(1) +-+ -- (- 8cos(1) |------ + (4sin(1) + 4cos(1))\|2 ) -- \|cos(1) -- * -- +------+ -- |sin(1) 2 +-+ -- 2cos(1)sin(1) |------ + (- cos(1)sin(1) + cos(1) - 1)\|2 -- \|cos(1) -- atan(-----------------------------------------------------------) -- +------+ -- 2 |sin(1) 2 +-+ -- 2cos(1) |------ + (- cos(1)sin(1) - cos(1) )\|2 -- \|cos(1) -- + -- +------+ -- |sin(1) +-+ -- (8cos(1) |------ + (- 4sin(1) - 4cos(1))\|2 ) -- \|cos(1) -- * -- +------+ -- |sin(1) 2 +-+ -- 4cos(1)sin(1) |------ + (- 2cos(1)sin(1) + 2cos(1) - 1)\|2 -- \|cos(1) -- atan(-------------------------------------------------------------) -- +------+ -- 2 |sin(1) 2 +-+ -- 4cos(1) |------ + (- 2cos(1)sin(1) - 2cos(1) + 1)\|2 -- \|cos(1) -- + -- +------+ -- |sin(1) +-+ -- (8cos(1) |------ + (- 4sin(1) - 4cos(1))\|2 ) -- \|cos(1) -- * -- +------+ -- |sin(1) 2 +-+ -- 2cos(1)sin(1) |------ + (- cos(1)sin(1) + cos(1) )\|2 -- \|cos(1) -- atan(-------------------------------------------------------) -- +------+ -- 2 |sin(1) 2 +-+ -- 2cos(1) |------ + (- cos(1)sin(1) - cos(1) + 1)\|2 -- \|cos(1) -- + -- +------+ -- |sin(1) -- (- 32sin(1) - 2cos(1)log(4) + (- 2%pi - 32)cos(1)) |------ -- \|cos(1) -- + -- +-+ -- ((log(4) + %pi + 32)sin(1) + cos(1)log(4) + %pi cos(1))\|2 -- / -- +------+ -- +-+ |sin(1) -- 16cos(1)\|2 |------ - 16sin(1) - 16cos(1) -- \|cos(1) -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1218a:=integrate(sin(z)*sec(z)/tan(z)^(1/2), z= 0..1,"noPole") -- -- +-+ -- 2\|2 -- * -- log -- 2 2 3 2 -- (- 16cos(1) sin(1) + (- 16cos(1) - 4cos(1))sin(1) - 4cos(1) ) -- * -- +------+ -- +-+ |sin(1) -- \|2 |------ -- \|cos(1) -- + -- 3 2 2 3 -- 8cos(1)sin(1) + 32cos(1) sin(1) + (8cos(1) + 8cos(1))sin(1) + 1 -- + -- +------+ -- |sin(1) 2 +-+ -- 2cos(1)sin(1) |------ + (- cos(1)sin(1) + cos(1) - 1)\|2 -- +-+ \|cos(1) -- 4\|2 atan(-----------------------------------------------------------) -- +------+ -- 2 |sin(1) 2 +-+ -- 2cos(1) |------ + (- cos(1)sin(1) - cos(1) )\|2 -- \|cos(1) -- + -- - -- +-+ -- 4\|2 -- * -- +------+ -- |sin(1) 2 +-+ -- 4cos(1)sin(1) |------ + (- 2cos(1)sin(1) + 2cos(1) - 1)\|2 -- \|cos(1) -- atan(-------------------------------------------------------------) -- +------+ -- 2 |sin(1) 2 +-+ -- 4cos(1) |------ + (- 2cos(1)sin(1) - 2cos(1) + 1)\|2 -- \|cos(1) -- + -- +------+ -- |sin(1) 2 +-+ -- 2cos(1)sin(1) |------ + (- cos(1)sin(1) + cos(1) )\|2 -- +-+ \|cos(1) -- - 4\|2 atan(-------------------------------------------------------) -- +------+ -- 2 |sin(1) 2 +-+ -- 2cos(1) |------ + (- cos(1)sin(1) - cos(1) + 1)\|2 -- \|cos(1) -- + -- +-+ -- %pi\|2 -- / -- 16 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1a:=integrate(log(abs(z^2-1))/(1+z)^2, z= 0..%plusInfinity,"noPole") -- -- 1 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in13:=integrate(cos(z)^2*sin(z)^n, z) -- -- z -- ++ 2 n -- | cos(%H) sin(%H) d%H -- ++ -- Type: Union(Expression Integer,...) in15ab:=integrate(log(sqrt(z)+z^5), z=0..a,"noPole") -- -- %pi -- 6cos(---) -- 9 -- * -- log -- %pi 6 +-+ %pi %pi 5 %pi 2 %pi 4 -- 2sin(---) + 4\|3 cos(---)sin(---) + 2cos(---) sin(---) -- 9 9 9 9 9 -- + -- +-+ %pi 3 %pi 3 %pi 4 %pi 2 -- 8\|3 cos(---) sin(---) + (- 2cos(---) + 2a)sin(---) -- 9 9 9 9 -- + -- +-+ %pi 5 +-+ %pi %pi %pi 6 -- (4\|3 cos(---) + 4a\|3 cos(---))sin(---) - 2cos(---) -- 9 9 9 9 -- + -- %pi 2 -- - 2a cos(---) -- 9 -- * -- +-+ -- \|a -- + -- %pi 8 %pi 2 %pi 6 %pi 4 %pi 4 -- sin(---) + 4cos(---) sin(---) + (6cos(---) + 3a)sin(---) -- 9 9 9 9 9 -- + -- +-+ %pi %pi 3 %pi 6 %pi 2 %pi 2 -- 4a\|3 cos(---)sin(---) + (4cos(---) + 14a cos(---) )sin(---) -- 9 9 9 9 9 -- + -- +-+ %pi 3 %pi %pi 8 %pi 4 2 -- - 4a\|3 cos(---) sin(---) + cos(---) + 3a cos(---) + a -- 9 9 9 9 -- + -- +-+ %pi %pi -- (- 3\|3 sin(---) - 3cos(---)) -- 9 9 -- * -- log -- %pi 6 +-+ %pi %pi 5 %pi 2 %pi 4 -- 2sin(---) - 4\|3 cos(---)sin(---) + 2cos(---) sin(---) -- 9 9 9 9 9 -- + -- +-+ %pi 3 %pi 3 %pi 4 %pi 2 -- - 8\|3 cos(---) sin(---) + (- 2cos(---) + 2a)sin(---) -- 9 9 9 9 -- + -- +-+ %pi 5 +-+ %pi %pi %pi 6 -- (- 4\|3 cos(---) - 4a\|3 cos(---))sin(---) - 2cos(---) -- 9 9 9 9 -- + -- %pi 2 -- - 2a cos(---) -- 9 -- * -- +-+ -- \|a -- + -- %pi 8 %pi 2 %pi 6 %pi 4 %pi 4 -- sin(---) + 4cos(---) sin(---) + (6cos(---) + 3a)sin(---) -- 9 9 9 9 9 -- + -- +-+ %pi %pi 3 %pi 6 %pi 2 %pi 2 -- - 4a\|3 cos(---)sin(---) + (4cos(---) + 14a cos(---) )sin(---) -- 9 9 9 9 9 -- + -- +-+ %pi 3 %pi %pi 8 %pi 4 2 -- 4a\|3 cos(---) sin(---) + cos(---) + 3a cos(---) + a -- 9 9 9 9 -- + -- 5 +-+ 10 +-+ -- 6a log(2a \|a + a + a) - 12log(\|a + 1) -- + -- +-+ 2 -- 3log((- 2a - 2)\|a + a + 3a + 1) -- + -- +-+ %pi %pi -- (3\|3 sin(---) - 3cos(---)) -- 9 9 -- * -- log -- %pi 6 %pi 2 %pi 4 -- - 4sin(---) - 4cos(---) sin(---) -- 9 9 9 -- + -- %pi 4 %pi 2 %pi 6 %pi 2 -- (4cos(---) - 4a)sin(---) + 4cos(---) + 4a cos(---) -- 9 9 9 9 -- * -- +-+ -- \|a -- + -- %pi 8 %pi 2 %pi 6 %pi 4 %pi 4 -- sin(---) + 4cos(---) sin(---) + (6cos(---) + 6a)sin(---) -- 9 9 9 9 9 -- + -- %pi 6 %pi 2 %pi 2 %pi 8 %pi 4 2 -- (4cos(---) - 4a cos(---) )sin(---) + cos(---) + 6a cos(---) + a -- 9 9 9 9 9 -- + -- %pi +-+ %pi -- (12sin(---) - 12\|3 cos(---)) -- 9 9 -- * -- +-+ %pi 2 %pi %pi +-+ %pi 2 -- \|3 sin(---) + 2cos(---)sin(---) - \|3 cos(---) -- 9 9 9 9 -- atan(-------------------------------------------------) -- %pi 2 +-+ %pi %pi %pi 2 -- sin(---) - 2\|3 cos(---)sin(---) - cos(---) -- 9 9 9 9 -- + -- +-+ +-+ +-+ -- +-+ 2\|3 \|a - \|3 -- 6\|3 atan(----------------) -- +-+ -- 2\|a - 2a + 1 -- + -- +-+ %pi 2 %pi %pi +-+ %pi 2 -- \|3 sin(---) - 2cos(---)sin(---) - \|3 cos(---) -- %pi 9 9 9 9 -- 24sin(---)atan(-------------------------------------------------) -- 9 %pi 2 +-+ %pi %pi %pi 2 -- sin(---) + 2\|3 cos(---)sin(---) - cos(---) -- 9 9 9 9 -- + -- %pi %pi -- 2cos(---)sin(---) -- %pi +-+ %pi 9 9 -- (12sin(---) + 12\|3 cos(---))atan(---------------------) -- 9 9 %pi 2 %pi 2 -- sin(---) - cos(---) -- 9 9 -- + -- %pi +-+ %pi -- (- 12sin(---) + 12\|3 cos(---)) -- 9 9 -- * -- +-+ %pi 2 %pi %pi +-+ %pi 2 -- \|3 sin(---) + 2cos(---)sin(---) - \|3 cos(---) -- 9 9 9 9 -- atan(-----------------------------------------------------) -- +-+ %pi 2 +-+ %pi %pi %pi 2 -- 2\|a + sin(---) - 2\|3 cos(---)sin(---) - cos(---) -- 9 9 9 9 -- + -- +-+ %pi 2 %pi %pi +-+ %pi 2 -- \|3 sin(---) - 2cos(---)sin(---) - \|3 cos(---) -- %pi 9 9 9 9 -- - 24sin(---)atan(-----------------------------------------------------) -- 9 +-+ %pi 2 +-+ %pi %pi %pi 2 -- 2\|a + sin(---) + 2\|3 cos(---)sin(---) - cos(---) -- 9 9 9 9 -- + -- %pi %pi -- 2cos(---)sin(---) -- %pi +-+ %pi 9 9 -- (12sin(---) + 12\|3 cos(---))atan(----------------------------) -- 9 9 +-+ %pi 2 %pi 2 -- \|a - sin(---) + cos(---) -- 9 9 -- + -- +-+ -- 2%pi\|3 - 60a -- / -- 12 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in20a:=integrate(log(sin(z)^2+cos(z)^2), z= 0..1,"noPole") -- -- 0 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in126a:=integrate(atan(1/cot(z)), z= 0..2*%pi,"noPole") -- -- 2 -- 2%pi -- Type: Union(f1: OrderedCompletion Expression Integer,...) in128a:=integrate(atan(sqrt(1-cos(z)^2)/(1+cos(z))), z= 0..1,"noPole") -- -- -- 1 -- - -- 4 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in134:=integrate(log(exp(z)), z= -%i..%i) -- -- 0 -- Type: Union(f1: OrderedCompletion Expression Integer,...) -- in134a:=integrate(log(exp(z)), z= -%i..%i) -- -- 0 -- Type: Union(f1: OrderedCompletion Expression Complex Integer,...) -- in1221a:=integrate(sin(z)*csc(z)*acoth(1/z), z= 0..1,"noPole") -- -- log(4) -- ------ -- 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1228a:=integrate(sin(z)*csc(z)*tan(z)^(1/2), z= 0..1,"noPole") -- -- +-+ -- 2\|2 -- * -- log -- 2 2 3 2 -- (- 16cos(1) sin(1) + (- 16cos(1) - 4cos(1))sin(1) - 4cos(1) ) -- * -- +------+ -- +-+ |sin(1) -- \|2 |------ -- \|cos(1) -- + -- 3 2 2 3 -- 8cos(1)sin(1) + 32cos(1) sin(1) + (8cos(1) + 8cos(1))sin(1) + 1 -- + -- +------+ -- |sin(1) 2 +-+ -- 2cos(1)sin(1) |------ + (- cos(1)sin(1) + cos(1) - 1)\|2 -- +-+ \|cos(1) -- 4\|2 atan(-----------------------------------------------------------) -- +------+ -- 2 |sin(1) 2 +-+ -- 2cos(1) |------ + (- cos(1)sin(1) - cos(1) )\|2 -- \|cos(1) -- + -- - -- +-+ -- 4\|2 -- * -- +------+ -- |sin(1) 2 +-+ -- 4cos(1)sin(1) |------ + (- 2cos(1)sin(1) + 2cos(1) - 1)\|2 -- \|cos(1) -- atan(-------------------------------------------------------------) -- +------+ -- 2 |sin(1) 2 +-+ -- 4cos(1) |------ + (- 2cos(1)sin(1) - 2cos(1) + 1)\|2 -- \|cos(1) -- + -- +------+ -- |sin(1) 2 +-+ -- 2cos(1)sin(1) |------ + (- cos(1)sin(1) + cos(1) )\|2 -- +-+ \|cos(1) -- - 4\|2 atan(-------------------------------------------------------) -- +------+ -- 2 |sin(1) 2 +-+ -- 2cos(1) |------ + (- cos(1)sin(1) - cos(1) + 1)\|2 -- \|cos(1) -- + -- +-+ -- %pi\|2 -- / -- 16 -- Type: Union(f1: OrderedCompletion Expression Integer,...) -- in1241a:=integrate(sin(z)*csc(z)*acoth(1/z), z= 0..1,"noPole") -- -- log(4) -- ------ -- 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1248a:=integrate(sin(z)*csc(z)*tan(z)^(1/2), z= 0..1,"noPole") -- -- +-+ -- 2\|2 -- * -- log -- 2 2 3 2 -- (- 16cos(1) sin(1) + (- 16cos(1) - 4cos(1))sin(1) - 4cos(1) ) -- * -- +------+ -- +-+ |sin(1) -- \|2 |------ -- \|cos(1) -- + -- 3 2 2 3 -- 8cos(1)sin(1) + 32cos(1) sin(1) + (8cos(1) + 8cos(1))sin(1) + 1 -- + -- +------+ -- |sin(1) 2 +-+ -- 2cos(1)sin(1) |------ + (- cos(1)sin(1) + cos(1) - 1)\|2 -- +-+ \|cos(1) -- 4\|2 atan(-----------------------------------------------------------) -- +------+ -- 2 |sin(1) 2 +-+ -- 2cos(1) |------ + (- cos(1)sin(1) - cos(1) )\|2 -- \|cos(1) -- + -- - -- +-+ -- 4\|2 -- * -- +------+ -- |sin(1) 2 +-+ -- 4cos(1)sin(1) |------ + (- 2cos(1)sin(1) + 2cos(1) - 1)\|2 -- \|cos(1) -- atan(-------------------------------------------------------------) -- +------+ -- 2 |sin(1) 2 +-+ -- 4cos(1) |------ + (- 2cos(1)sin(1) - 2cos(1) + 1)\|2 -- \|cos(1) -- + -- +------+ -- |sin(1) 2 +-+ -- 2cos(1)sin(1) |------ + (- cos(1)sin(1) + cos(1) )\|2 -- +-+ \|cos(1) -- - 4\|2 atan(-------------------------------------------------------) -- +------+ -- 2 |sin(1) 2 +-+ -- 2cos(1) |------ + (- cos(1)sin(1) - cos(1) + 1)\|2 -- \|cos(1) -- + -- +-+ -- %pi\|2 -- / -- 16 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1261a:=integrate(1/(sin(z)+cos(2*z)), z= -1..1,"noPole") -- -- 2 2 -- (- sin(1) + cos(1) + 2cos(1) + 1) -- * -- log -- 2 2 -- - 12sin(1) + (42cos(1) + 48)sin(1) - 36cos(1) - 84cos(1) -- + -- - 48 -- * -- +-+ -- \|3 -- + -- 2 2 -- 21sin(1) + (- 72cos(1) - 84)sin(1) + 63cos(1) + 144cos(1) + 84 -- / -- 2 -- 4sin(1) - 4sin(1) + 1 -- + -- 2 2 -- (sin(1) - cos(1) - 2cos(1) - 1) -- * -- log -- 2 2 -- - 12sin(1) + (- 42cos(1) - 48)sin(1) - 36cos(1) - 84cos(1) -- + -- - 48 -- * -- +-+ -- \|3 -- + -- 2 2 -- 21sin(1) + (72cos(1) + 84)sin(1) + 63cos(1) + 144cos(1) + 84 -- / -- 2 -- 4sin(1) + 4sin(1) + 1 -- + -- +-+ -- (- 4cos(1) - 4)sin(1)\|3 -- / -- 2 2 +-+ -- (3sin(1) - 3cos(1) - 6cos(1) - 3)\|3 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1273a:=integrate((1/(z-I))^(1/2), z= 0..%plusInfinity,"noPole") -- -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1274a:=integrate(1/(1/(z-I))^(1/2), z= 0..%plusInfinity,"noPole") -- -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1278a:=integrate((1+1/(I*z)^(1/2))^(1/2), z= 0..%plusInfinity,"noPole") -- -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1284a:=integrate(log(1+2^(1/2)/z^(1/4)-1/z^(1/2)), z= 0..%plusInfinity,"noPole") -- -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1314a:=integrate(log(1-z)*atanh(z^(1/2)), z= 0..1,"noPole") -- log(16) - 6 -- ----------- -- 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1359a:=integrate((I*z)^(1/2)*(-I*z)^(1/2), z= %minusInfinity..%plusInfinity,"noPole") -- -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1376a:=integrate(z*acoth(z^(1/2)), z= 0..1,"noPole") -- -- 2 -- - -- 3 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1377a:=integrate(z*acoth(1-z), z= 0..1,"noPole") -- -- log(4) - 1 -- ---------- -- 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1378a:=integrate(z*acoth(1-(1-z)^(1/2)), z= 0..1,"noPole") -- -- - 3log(4) + 5 -- ------------- -- 3 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1392a:=integrate(acoth(z^(1/2)), z= 0..1,"noPole") -- -- 1 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1397a:=integrate(1/(-1+z^(1/2))^(1/2), z= 1..2,"noPole") -- -- +--------+ -- +-+ | +-+ -- (4\|2 + 8)\|\|2 - 1 -- ---------------------- -- 3 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1398a:=integrate(acoth(1/z), z= 1..2,"noPole") -- -- 3log(9) - 2log(4) -- ----------------- -- 4 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1399a:=integrate(acoth(1/z^(1/2)), z= 1..2,"noPole") -- -- +-+ -- - 2\|2 - 3 +-+ -- log(-----------) + 4\|2 - 4 -- +-+ -- 2\|2 - 3 -- ---------------------------- -- 4 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in143a:=integrate(sqrt(1+z)/(1+z^2), z= 0..1,"noPole") -- -- 4+-+ %pi -- \|2 cos(---) -- 8 -- * -- log -- %pi 4 +-+4+-+3 %pi 3 %pi 2 4+-+2 %pi 2 -- 2sin(---) + 4\|2 \|2 sin(---) + (4cos(---) + 12\|2 )sin(---) -- 8 8 8 8 -- + -- +-+4+-+3 %pi 2 +-+4+-+ %pi %pi 4 -- (4\|2 \|2 cos(---) + 8\|2 \|2 )sin(---) + 2cos(---) -- 8 8 8 -- + -- 4+-+2 %pi 2 -- 4\|2 cos(---) + 4 -- 8 -- + -- - -- 4+-+ %pi -- \|2 cos(---) -- 8 -- * -- log -- %pi 4 4+-+3 %pi 3 %pi 2 4+-+2 %pi 2 -- 2sin(---) + 4\|2 sin(---) + (4cos(---) + 6\|2 )sin(---) -- 8 8 8 8 -- + -- 4+-+3 %pi 2 4+-+ %pi %pi 4 -- (4\|2 cos(---) + 4\|2 )sin(---) + 2cos(---) -- 8 8 8 -- + -- 4+-+2 %pi 2 -- 2\|2 cos(---) + 1 -- 8 -- + -- 4+-+ %pi -- \|2 cos(---) -- 8 -- * -- log -- %pi 4 4+-+3 %pi 3 %pi 2 4+-+2 %pi 2 -- 2sin(---) - 4\|2 sin(---) + (4cos(---) + 6\|2 )sin(---) -- 8 8 8 8 -- + -- 4+-+3 %pi 2 4+-+ %pi %pi 4 4+-+2 %pi 2 -- (- 4\|2 cos(---) - 4\|2 )sin(---) + 2cos(---) + 2\|2 cos(---) -- 8 8 8 8 -- + -- 1 -- + -- - -- 4+-+ %pi -- \|2 cos(---) -- 8 -- * -- log -- %pi 4 +-+4+-+3 %pi 3 -- 2sin(---) - 4\|2 \|2 sin(---) -- 8 8 -- + -- %pi 2 4+-+2 %pi 2 -- (4cos(---) + 12\|2 )sin(---) -- 8 8 -- + -- +-+4+-+3 %pi 2 +-+4+-+ %pi %pi 4 -- (- 4\|2 \|2 cos(---) - 8\|2 \|2 )sin(---) + 2cos(---) -- 8 8 8 -- + -- 4+-+2 %pi 2 -- 4\|2 cos(---) + 4 -- 8 -- + -- 4+-+ %pi -- \|2 cos(---) -- 4+-+ %pi 8 -- - 4\|2 sin(---)atan(-------------------) -- 8 4+-+ %pi +-+ -- \|2 sin(---) - \|2 -- 8 -- + -- 4+-+ %pi 4+-+ %pi -- \|2 cos(---) \|2 cos(---) -- 4+-+ %pi 8 4+-+ %pi 8 -- 4\|2 sin(---)atan(----------------) - 4\|2 sin(---)atan(----------------) -- 8 4+-+ %pi 8 4+-+ %pi -- \|2 sin(---) - 1 \|2 sin(---) + 1 -- 8 8 -- + -- 4+-+ %pi -- \|2 cos(---) -- 4+-+ %pi 8 -- 4\|2 sin(---)atan(-------------------) -- 8 4+-+ %pi +-+ -- \|2 sin(---) + \|2 -- 8 -- / -- 4 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in144:=integrate(1, z= I*infinity..%plusInfinity) -- -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in146a:=integrate(csc(z), z= 1-%i..1+%i,"noPole") -- -- 2 2 -- sin(I + 1) sin(I - 1) -- log(-----------------------------) - log(-----------------------------) -- 2 2 -- cos(I + 1) + 2cos(I + 1) + 1 cos(I - 1) + 2cos(I - 1) + 1 -- ----------------------------------------------------------------------- -- 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in148:=integrate(min(1,z), z= 0..2) -- -- 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in156a:=integrate(z^(2/3), z= 1..10,"noPole") -- -- 3+--+2 -- 30\|10 - 3 -- ------------ -- 5 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in159a:=integrate(log(z)/z^2, z= -%i..-1,"noPole") -- -- 2 -- - log(I ) + 2I - 2 -- ------------------ -- 2I -- Type: Union(f1: OrderedCompletion Expression Integer,...) in160:=integrate((-z^2-z)^sin(z), z) -- -- z -- ++ 2 sin(%R) -- | (- %R - %R) d%R -- ++ -- Type: Union(Expression Integer,...) in1425a:=integrate(-(z^2+I*z+3)/(z^2+I*z+2), z= 0..%plusInfinity,"noPole") -- -- [- infinity,- infinity] -- Type: Union(f2: List OrderedCompletion Expression Integer,...) in1426a:=integrate(-I/(1+I*z^3)*z^3, z= 0..%plusInfinity,"noPole") -- -- - infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1428a:=integrate(-I/(1+I*z)*z, z= 0..%plusInfinity,"noPole") -- -- - infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1432:=integrate(-(z+I)*(-1+1/(z+I)), z= 0..%plusInfinity) -- -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1433a:=integrate(-1/((I*z)^(1/2)-1)*(-2+(I*z)^(1/2)), z= 0..%plusInfinity,"noPole") -- -- - infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1434a:=integrate(-(1+(I*z)^(1/2))/(I*z)^(1/2), z= 0..%plusInfinity,"noPole") -- -- - infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1435a:=integrate(-1/(1+(I*z)^(1/2))*(I*z)^(1/2), z= 0..%plusInfinity,"noPole") -- -- - infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1436a:=integrate(-((I*z)^(1/2)-1)/(-2+(I*z)^(1/2)), z= 0..%plusInfinity,"noPole") -- -- - infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1440a:=integrate((1-(I*z)^(1/2))/(I*z)^(1/2), z= 0..%plusInfinity,"noPole") -- -- - infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1460:=integrate(z^2+I*z+3, z= 0..%plusInfinity) -- -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1463a:=integrate(1-(I*z)^(1/2)/(1-I*z), z= 0..%plusInfinity,"noPole") -- -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1464a:=integrate(1+1/(I*z)^(1/2), z= 0..%plusInfinity,"noPole") -- -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2045:=integrate(atan(1/tan(z)), z= 0..2*%pi) -- -- 2 -- - 3%pi -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1502a:=integrate(log(z)^2*log(-z), z= 0..%plusInfinity) -- -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1512a:=integrate(log(z)*(1/(z-I))^(1/2), z= 1..%plusInfinity,"noPole") -- -- [ + infinity, + infinity] -- Type: Union(f2: List OrderedCompletion Expression Integer,...) in1513a:=integrate(log(z)*(1/(z+I))^(1/2), z= 1..%plusInfinity,"noPole") -- -- [ + infinity, + infinity] -- Type: Union(f2: List OrderedCompletion Expression Integer,...) in1514a:=integrate(log(z)/(I/(z-I))^(1/2), z= 1..%plusInfinity,"noPole") -- -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1563a:=integrate(log(1-z^3)*(I*z)^(1/2), z= 0..1,"noPole") -- -- 2 -- 16I 2 +-+ -- (log(----) - log(I ) + log(9) - 4)\|I -- 9 -- [--------------------------------------,- infinity] -- 3 -- Type: Union(f2: List OrderedCompletion Expression Integer,...) in161:=integrate((-z^2)^(1/3), z) -- +----+ -- 3| 2 -- 3z\|- z -- (81) --------- -- 5 -- Type: Union(Expression Integer,...) in163:=integrate(log(z)*abs(exp(z)/z), z) -- -- z %K -- ++ %e -- | log(%K)abs(----)d%K -- ++ %K -- Type: Union(Expression Integer,...) in166:=integrate((1+z)^z, z) -- -- z -- ++ %K -- | (%K + 1) d%K -- ++ -- Type: Union(Expression Integer,...) in179:=integrate(1/(1+(3*z+1)^2), z) -- -- atan(3z + 1) -- ------------ -- 3 -- Type: Union(Expression Integer,...) in1636a:=integrate(-z/(z-1)/(1/(z-I))^(1/2), z= 0..1,"noPole") -- -- [ + infinity, -- -- +-------+ +---+ -- +-----+ \|- I + 1 +-----+ \|- I -- 6\|I - 1 log(- ----------) - 6\|I - 1 atan(--------) -- +-----+ +-----+ -- 2\|I - 1 \|I - 1 -- + -- +-------+ +---+ -- (2I - 8)\|- I + 1 + (- 2I + 6)\|- I -- / -- 3 -- ] -- Type: Union(f2: List OrderedCompletion Expression Integer,...) -- in1638a:=integrate(-z/(z-1)/(1-I*z)^(1/2), z= 0..1,"noPole") -- -- [ + infinity, -- -- +-------+ +-----+ +-----+ -- \|- I + 1 \|I - 1 \|I - 1 -- - 2I log(- ------------------) + 2I atan(--------) -- 2I - 2 I - 1 -- + -- +-------+ +-----+ -- (2\|- I + 1 - 2)\|I - 1 -- / -- +-----+ -- I\|I - 1 -- ] -- Type: Union(f2: List OrderedCompletion Expression Integer,...) in1639a:=integrate(-z/(z-1)/(1-I*z^2)^(1/2), z= 0..1,"noPole") -- -- [ + infinity, -- -- +-----+ -- \|I - 1 -- * -- log -- 2 +---+ 2 +-------+ 2 +---+ -- ((2I - 4I)\|- I + 4I - 2I)\|- I + 1 + (- 4I + 4I)\|- I -- + -- 3 2 -- 2I - 5I + 2I -- / -- +-------+ -- 2\|- I + 1 + I - 2 -- + -- +-------+ +-----+ +-----+ -- +---+ (- \|- I + 1 - I + 1)\|I - 1 +---+ \|I - 1 -- 4\|- I log(------------------------------) + 4\|- I atan(--------) -- +-------+ I - 1 -- (2I - 2)\|- I + 1 - 2I + 2 -- + -- +-----+ -- - log(- I)\|I - 1 -- / -- +---+ +-----+ -- 2\|- I \|I - 1 -- , -- + infinity, -- -- +-------+ +-----+ -- +-+ (- \|- I + 1 - I + 1)\|I - 1 -- 2\|I log(------------------------------) -- +-------+ -- (2I - 2)\|- I + 1 - 2I + 2 -- + -- +-------+ +-+ +-----+ -- +-----+ (\|- I + 1 - 1)\|I +-+ \|I - 1 -- 2\|I - 1 atan(--------------------) + 2\|I atan(--------) -- I I - 1 -- / -- +-----+ +-+ -- \|I - 1 \|I -- ] -- Type: Union(f2: List OrderedCompletion Expression Integer,...) in1712a:=integrate(-log(-z)*(-I*z)^(1/2), z= 0..1,"noPole") -- -- +---+ -- 4\|- I -- ------- -- 9 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1720a:=integrate(-z^2/(z^2-1)*(1/(z-I))^(1/2), z= 0..1,"noPole") -- -- [ + infinity, -- -- +-----+ 2 +-------+ +---+ 3 2 -- - \|I - 1 log((- 8I - 12I - 4)\|- I - 1 \|- I - 8I - 16I - 9I - 1) -- + -- +-----+ 2 +-------+ +-------+ 3 2 -- \|I - 1 log((- 2I - 2I)\|- I - 1 \|- I + 1 - 2I - 2I + I + 1) -- + -- +-------+ +-----+ -- +-------+ \|- I + 1 \|I - 1 -- - 4\|- I - 1 log(- ------------------) -- 2I - 2 -- + -- +---+ +-----+ -- +-------+ \|- I \|I - 1 -- 4\|- I - 1 atan(--------------) -- I - 1 -- + -- +-------+ +-------+ +-------+ +---+ +-----+ -- (- 8\|- I - 1 \|- I + 1 + 8\|- I - 1 \|- I )\|I - 1 -- / -- +-------+ +-----+ -- 4\|- I - 1 \|I - 1 -- , -- + infinity, -- -- +-------+ +-----+ +-------+ +-----+ -- +-----+ \|- I + 1 \|I - 1 +-----+ \|- I + 1 \|I + 1 -- - \|I + 1 log(- ------------------) + \|I - 1 atan(------------------) -- 2I - 2 I + 1 -- + -- +---+ +-----+ +---+ +-----+ -- +-----+ \|- I \|I + 1 +-----+ \|- I \|I - 1 -- - \|I - 1 atan(--------------) + \|I + 1 atan(--------------) -- I + 1 I - 1 -- + -- +-------+ +---+ +-----+ +-----+ -- (- 2\|- I + 1 + 2\|- I )\|I - 1 \|I + 1 -- / -- +-----+ +-----+ -- \|I - 1 \|I + 1 -- ] -- Type: Union(f2: List OrderedCompletion Expression Integer,...) in1721a:=integrate(-z^2/(z^2-1)/(1/(z-I))^(1/2), z= 0..1,"noPole") -- -- [ + infinity, + infinity, -- -- +-------+ +-------+ +-------+ 2 -- 3\|- I - 1 log(2I\|- I - 1 \|- I + 1 + 2I - 1) -- + -- +-------+ +-------+ +---+ 2 -- - 3\|- I - 1 log((8I + 4)\|- I - 1 \|- I + 8I + 8I + 1) -- + -- +-------+ +---+ -- +-----+ \|- I + 1 +-----+ \|- I -- 12\|I - 1 log(- ----------) - 12\|I - 1 atan(--------) -- +-----+ +-----+ -- 2\|I - 1 \|I - 1 -- + -- +-------+ +---+ -- (8I - 8)\|- I + 1 - 8I\|- I -- / -- 12 -- , -- -- +-------+ +---+ -- +-----+ \|- I + 1 +-----+ \|- I -- 3\|I - 1 log(- ----------) - 3\|I - 1 atan(--------) -- +-----+ +-----+ -- 2\|I - 1 \|I - 1 -- + -- +-------+ +---+ -- +-----+ \|- I + 1 +-----+ \|- I -- - 3\|I + 1 atan(----------) + 3\|I + 1 atan(--------) -- +-----+ +-----+ -- \|I + 1 \|I + 1 -- + -- +-------+ +---+ -- (2I - 2)\|- I + 1 - 2I\|- I -- / -- 3 -- ] -- Type: Union(f2: List OrderedCompletion Expression Integer,...) in1723a:=integrate(-z^2/(z^2-1)*(1+I/z)^(1/2), z= 0..1,"noPole") -- -- [ + infinity, + infinity, -- -- +-----+ -- +-----+ +-+ +-------+ \|I + 1 -- - 2I log(\|I + 1 + 1) + 2I log(\|I ) + 4\|- I - 1 log(- -----------) -- +-------+ -- 2\|- I - 1 -- + -- +-----+ -- I log(- 2\|I + 1 + I + 2) -- + -- +-------+ +-------+ +-----+ 2 +-----+ -- \|- I + 1 log(- 2\|- I + 1 \|I + 1 - I + 2) - 4\|I + 1 -- + -- 2 +-------+ +-------+ -- - log(I )\|- I + 1 - 2%pi\|- I - 1 - I log(I) -- / -- 4 -- , -- -- +-----+ -- +-----+ +-+ +-------+ \|I + 1 -- - 2I log(\|I + 1 + 1) + 2I log(\|I ) + 4\|- I - 1 log(- -----------) -- +-------+ -- 2\|- I - 1 -- + -- +-----+ -- +-----+ +-----+ \|I - 1 +-----+ -- I log(- 2\|I + 1 + I + 2) + 4\|I - 1 atan(--------) - 4\|I + 1 -- +-----+ -- \|I + 1 -- + -- +-------+ -- - 2%pi\|- I - 1 - I log(I) -- / -- 4 -- ] -- Type: Union(f2: List OrderedCompletion Expression Integer,...) in1724a:=integrate(-z^2/(z^2-1)*(1-(I*z)^(1/2))^(1/2), z= 0..1,"noPole") -- -- +----------+ -- +-+ | +-+ -- (4\|I - 12I + 8)\|- \|I + 1 - 8 -- ---------------------------------- -- 15I -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1731:=integrate(-log(1-z^2)*atanh(z), z= 0..1) -- -- 2 -- - log(4) + 4log(4) -- ------------------- -- 4 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1793a:=integrate((1-z^(1/2))^(1/2)*acoth(z^(1/2)), z= 0..1,"noPole") -- -- +-+ +-+ -- - 2\|2 log(12\|2 + 17) + 16 -- ---------------------------- -- 15 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1794a:=integrate((1-z^(1/2))^(1/2)*acoth(1-z^(1/2)), z= 0..1,"noPole") -- -- - 4log(2) - 8%pi + 32 -- --------------------- -- 15 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1796a:=integrate((1+(1-z)^(1/2))^(1/2), z= 0..1,"noPole") -- -- +-+ -- 8\|2 + 8 -- --------- -- 15 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in183:=integrate(1/z, z= %i..2*%i) -- -- 2 2 -- log(4I ) - log(I ) -- ------------------ -- 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in184:=integrate(exp(I*z), z= %i..2*%i) -- -- 2 2 -- 2I I -- %e - %e -- (29) ------------ -- I -- Type: Union(f1: OrderedCompletion Expression Integer,...) in184a:=integrate(exp(%i*z), z= %i..2*%i) -- -- 2 -- %i %e - %i %e -- (30) -------------- -- 2 -- %e %e -- Type: Union(f1: OrderedCompletion Expression Complex Integer,...) in187a:=integrate(2^log(z), z= -%i..%i,"noPole") -- -- log(2)log(I) log(2)log(- I) -- I %e + I %e -- ------------------------------------- -- log(2) + 1 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in187a:=integrate(2^log(z), z= -%i..%i,"noPole") -- -- log(%i)log(2) log(- %i)log(2) -- %i %e + %i %e -- ----------------------------------------- -- log(2) + 1 -- Type: Union(f1: OrderedCompletion Expression Complex Integer,...) in194a:=integrate(sqrt(z^2), z= 1..2,"noPole") -- -- 3 -- (43) - -- 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1854a:=integrate(1/(z-1)/(1/(z-I))^(1/2), z= 0..1,"noPole") -- -- [- infinity, -- -- +-------+ +---+ -- +-----+ \|- I + 1 +-----+ \|- I +-------+ -- - 2\|I - 1 log(- ----------) + 2\|I - 1 atan(--------) + 2\|- I + 1 -- +-----+ +-----+ -- 2\|I - 1 \|I - 1 -- + -- +---+ -- - 2\|- I -- ] -- Type: Union(f2: List OrderedCompletion Expression Integer,...) in1856a:=integrate(1/(z-1)/(1-I*z)^(1/2), z= 0..1,"noPole") -- -- +-------+ +-----+ +-----+ -- \|- I + 1 \|I - 1 \|I - 1 -- 2log(- ------------------) - 2atan(--------) -- 2I - 2 I - 1 -- [- infinity,--------------------------------------------] -- +-----+ -- \|I - 1 -- Type: Union(f2: List OrderedCompletion Expression Integer,...) in1859a:=integrate(1/(z^2-1)*(1+1/z^3)^(1/2), z= 0..1,"noPole") -- -- +-------------------+ -- | 2 -- (- \|- 3%%EM0 - 2 + 6%i - %%EM0) -- * -- log -- +--+ +--+ -- ((8 + 72%i)\|%i + 10 + 8%i)%%EM0 + (- 2 - 18%i)\|%i + 2 -- + -- 18%i -- * -- +-------------------+ -- | 2 -- \|- 3%%EM0 - 2 + 6%i -- + -- +--+ 2 -- ((- 8 - 72%i)\|%i - 10 - 8%i)%%EM0 -- + -- +--+ +--+ -- ((- 2 - 18%i)\|%i + 2 + 18%i)%%EM0 + (- 128 - 4%i)\|%i - 68 -- + -- - 120%i -- + -- +-------------------+ -- | 2 -- (\|- 3%%EM0 - 2 + 6%i + %%EM0) -- * -- log -- +-------------------+ -- | 2 -- ((10 + 8%i)%%EM0 + 2 + 18%i)\|- 3%%EM0 - 2 + 6%i -- + -- 2 -- (- 10 - 8%i)%%EM0 + (2 + 18%i)%%EM0 - 50 - 40%i -- + -- +-------------------+ -- | 2 -- (- \|- 3%%EM0 - 2 + 6%i + %%EM0) -- * -- log -- +-------------------+ -- | 2 -- ((- 10 - 8%i)%%EM0 - 2 - 18%i)\|- 3%%EM0 - 2 + 6%i -- + -- 2 -- (- 10 - 8%i)%%EM0 + (2 + 18%i)%%EM0 - 50 - 40%i -- + -- +-------------------+ -- | 2 -- (\|- 3%%EM0 - 2 + 6%i - %%EM0) -- * -- log -- +--+ +--+ -- ((- 8 - 72%i)\|%i - 10 - 8%i)%%EM0 + (2 + 18%i)\|%i - 2 -- + -- - 18%i -- * -- +-------------------+ -- | 2 -- \|- 3%%EM0 - 2 + 6%i -- + -- +--+ 2 -- ((- 8 - 72%i)\|%i - 10 - 8%i)%%EM0 -- + -- +--+ +--+ -- ((- 2 - 18%i)\|%i + 2 + 18%i)%%EM0 + (- 128 - 4%i)\|%i - 68 -- + -- - 120%i -- + -- 2%%EM0 -- * -- log -- +--+ 2 -- ((72 - 8%i)\|%i + 8 - 10%i)%%EM0 -- + -- +--+ +--+ -- ((18 - 2%i)\|%i - 18 + 2%i)%%EM0 + (22 - 48%i)\|%i - 71 + 17%i -- + -- 2 -- - 2%%EM0 log((8 - 10%i)%%EM0 + (- 18 + 2%i)%%EM0 - 31 + 8%i) -- / -- 4 -- Type: Union(f1: OrderedCompletion Expression Complex Integer,...) in1863a:=integrate(1/(z^2-1)*(1/(z-I))^(1/2), z= 0..1,"noPole") -- [- infinity, -- -- +-----+ 2 +-------+ +-------+ 3 2 -- \|I - 1 log((2I + 2I)\|- I - 1 \|- I + 1 - 2I - 2I + I + 1) -- + -- +-----+ 2 +-------+ +---+ 3 2 -- - \|I - 1 log((8I + 12I + 4)\|- I - 1 \|- I - 8I - 16I - 9I - 1) -- + -- +-------+ +-----+ +---+ +-----+ -- +-------+ \|- I + 1 \|I - 1 +-------+ \|- I \|I - 1 -- 4\|- I - 1 log(- ------------------) - 4\|- I - 1 atan(--------------) -- 2I - 2 I - 1 -- / -- +-------+ +-----+ -- 4\|- I - 1 \|I - 1 -- , -- - infinity, -- -- +-------+ +-----+ +-------+ +-----+ -- +-----+ \|- I + 1 \|I - 1 +-----+ \|- I + 1 \|I + 1 -- \|I + 1 log(- ------------------) - \|I - 1 atan(------------------) -- 2I - 2 I + 1 -- + -- +---+ +-----+ +---+ +-----+ -- +-----+ \|- I \|I + 1 +-----+ \|- I \|I - 1 -- \|I - 1 atan(--------------) - \|I + 1 atan(--------------) -- I + 1 I - 1 -- / -- +-----+ +-----+ -- \|I - 1 \|I + 1 -- ] -- Type: Union(f2: List OrderedCompletion Expression Integer,...) in1864a:=integrate(1/(z^2-1)*((1+z)/(z-1))^(1/3), z= 0..1,"noPole") -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1866a:=integrate(1/(z^2-1)*(1-I/z)^(1/2), z= 0..1,"noPole") -- [- infinity, -- -- +-----+ -- +-----+ +-------+ +-----+ 2 +-----+ \|I - 1 -- \|I + 1 log(2\|- I + 1 \|I + 1 - I + 2) + 4\|I - 1 log(- -----------) -- +-------+ -- 2\|- I + 1 -- + -- 2 +-----+ -- - log(I )\|I + 1 -- / -- 4 -- , -- - infinity, -- +-----+ +-------+ -- +-----+ \|I - 1 +-------+ \|- I + 1 +-------+ -- 2\|I - 1 log(- -----------) + 2\|- I - 1 atan(----------) - %pi\|- I - 1 -- +-------+ +-------+ -- 2\|- I + 1 \|- I - 1 -- -------------------------------------------------------------------------] -- 2 -- Type: Union(f2: List OrderedCompletion Expression Integer,...) in1867a:=integrate(1/(z^2-1)*(1-(I*z)^(1/2))^(1/2), z= 0..1,"noPole") -- 0 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1869a:=integrate(1/(z^2-1)*(1-1/(I*z)^(1/2))^(1/2), z= 0..1,"noPole") -- 0 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1870a:=integrate(1/(z^2-1)/(1+(I*z)^(1/2))^(1/2), z= 0..1,"noPole") -- 0 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1872a:=integrate(1/(z^2-1)/(I/(z+I))^(1/2), z= 0..1,"noPole") -- -- [ + infinity, + infinity, -- -- +-----+ +-----+ +-----+ -- |I - 1 2 |I - 1 | I 2 -- |----- log((2I + 2I) |----- |----- + 2I - 1) -- \| I \| I \|I + 1 -- + -- +-----+ +-----+ -- |I - 1 2 |I - 1 2 -- - |----- log((8I - 4I) |----- + 8I - 8I + 1) -- \| I \| I -- + -- +-----+ -- | I -- +-------+ (- I - 1) |----- +-------+ -- |- I - 1 \|I + 1 |- I - 1 I + 1 -- - 4 |------- log(----------------- + 4 |------- atan(-----------) -- \| I +-------+ \| I +-------+ -- |- I - 1 |- I - 1 -- 2I |------- I |------- -- \| I \| I -- / -- 4 -- , -- -- +-----+ +-----+ -- | I | I -- +-------+ (- I - 1) |----- +-------+ (I - 1) |----- -- |- I - 1 \|I + 1 |- I + 1 \|I + 1 -- - |------- log(-----------------) + |------- atan(---------------) -- \| I +-------+ \| I +-------+ -- |- I - 1 |- I + 1 -- 2I |------- I |------- -- \| I \| I -- + -- +-------+ +-------+ -- |- I - 1 I + 1 |- I + 1 I - 1 -- |------- atan(-----------) - |------- atan(-----------) -- \| I +-------+ \| I +-------+ -- |- I - 1 |- I + 1 -- I |------- I |------- -- \| I \| I -- ] -- Type: Union(f2: List OrderedCompletion Expression Integer,...) in1933a:=integrate(atan(z)/z/(z*(1+z))^(1/2), z= 0..1,"noPole") -- -- +-+ 4+-+ %pi -- (\|2 - 1)\|2 cos(---) -- 8 -- * -- 4+-+2 %pi 2 4+-+3 4+-+ %pi 4+-+2 -- log(4\|2 sin(---) + (4\|2 + 4\|2 )sin(---) + 2\|2 + 3) -- 8 8 -- + -- +-+ 4+-+ %pi -- (- \|2 + 1)\|2 cos(---) -- 8 -- * -- 4+-+2 %pi 2 4+-+3 4+-+ %pi 4+-+2 -- log(4\|2 sin(---) + (- 4\|2 - 4\|2 )sin(---) + 2\|2 + 3) -- 8 8 -- + -- +-+ 4+-+ %pi -- (- \|2 + 1)\|2 cos(---) -- 8 -- * -- log -- 4+-+2 %pi 2 -- 4\|2 sin(---) -- 8 -- + -- +-+ 4+-+2 %pi 4+-+3 +-+ 4+-+ %pi -- ((- 8\|2 + 8)\|2 cos(---) + 4\|2 + (- 8\|2 + 16)\|2 )sin(---) -- 8 8 -- + -- +-+ 4+-+2 %pi 2 -- (- 8\|2 + 12)\|2 cos(---) -- 8 -- + -- +-+ 4+-+3 +-+ 4+-+ %pi -- ((- 4\|2 + 4)\|2 + (- 24\|2 + 32)\|2 )cos(---) -- 8 -- + -- +-+ 4+-+2 +-+ -- (- 4\|2 + 8)\|2 - 16\|2 + 26 -- + -- +-+ 4+-+ %pi -- (\|2 - 1)\|2 cos(---) -- 8 -- * -- log -- 4+-+2 %pi 2 -- 4\|2 sin(---) -- 8 -- + -- +-+ 4+-+2 %pi 4+-+3 +-+ 4+-+ %pi -- ((- 8\|2 + 8)\|2 cos(---) - 4\|2 + (8\|2 - 16)\|2 )sin(---) -- 8 8 -- + -- +-+ 4+-+2 %pi 2 -- (- 8\|2 + 12)\|2 cos(---) -- 8 -- + -- +-+ 4+-+3 +-+ 4+-+ %pi -- ((4\|2 - 4)\|2 + (24\|2 - 32)\|2 )cos(---) -- 8 -- + -- +-+ 4+-+2 +-+ -- (- 4\|2 + 8)\|2 - 16\|2 + 26 -- + -- 4+-+ %pi -- \|2 sin(---) + 1 -- +-+ 4+-+ %pi 8 -- (4\|2 - 4)\|2 sin(---)atan(-----------------------) -- 8 4+-+ %pi +-+ -- \|2 cos(---) - \|2 + 1 -- 8 -- + -- 4+-+ %pi -- \|2 sin(---) + 1 -- +-+ 4+-+ %pi 8 -- (- 4\|2 + 4)\|2 sin(---)atan(----------------) -- 8 4+-+ %pi -- \|2 cos(---) -- 8 -- + -- 4+-+ %pi -- \|2 sin(---) - 1 -- +-+ 4+-+ %pi 8 -- (4\|2 - 4)\|2 sin(---)atan(----------------) -- 8 4+-+ %pi -- \|2 cos(---) -- 8 -- + -- 4+-+ %pi -- \|2 sin(---) - 1 -- +-+ 4+-+ %pi 8 +-+ -- (- 4\|2 + 4)\|2 sin(---)atan(-----------------------) + %pi\|2 - 2%pi -- 8 4+-+ %pi +-+ -- \|2 cos(---) + \|2 - 1 -- 8 -- / -- +-+ -- 2\|2 - 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1945a:=integrate(acoth((1-z)/(1+z)), z= 0..1,"noPole") -- -- 1 -- - -- 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1946a:=integrate(acoth((1-z)/(1+z))*z, z= 0..1,"noPole") -- -- 1 -- - -- 8 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1947a:=integrate(acoth((1-z)/(1+z))*z^(1/2), z= 0..1,"noPole") -- -- 2 -- - -- 9 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1950a:=integrate(acoth((1-z)/(1+z))/(1-z)^(1/2), z= 0..1,"noPole") -- -- - log(4) - 2log(2) + 4 -- ---------------------- -- 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1952a:=integrate(acoth((1-z)/(1+z))*(I*z)^(1/2), z= 0..1,"noPole") -- -- +-+ -- 2\|I -- ----- -- 9 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in1954a:=integrate(acoth((1-z)/(1+z))/(I*z)^(1/2), z= 0..1,"noPole") -- -- +-+ -- 2\|I -- ----- -- I -- Type: Union(f1: OrderedCompletion Expression Integer,...) in202a:=integrate(acsc(z), z= 0..1/2,"noPole") -- -- +-+ +-+ -- +-+ 2\|2 \|3 +-+ -- - 6\|2 atan(---------) - 3atan(4\|3 ) + 2%pi -- 5 -- -------------------------------------------- -- 12 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in206a:=integrate(sqrt(1-1/z), z= %pi..2*%pi,"noPole") -- -- +--------+ +-------+ -- |2%pi - 1 |%pi - 1 -- - 2log( |-------- + 1) + 2log( |------- + 1) -- \| 2%pi \| %pi -- + -- +-------+ +--------+ -- |%pi - 1 |2%pi - 1 -- - 2%pi |------- + 2%pi - 1 - 4%pi |-------- + 4%pi - 1 -- \| %pi \| 2%pi -- - log(---------------------------) + log(----------------------------) -- %pi 2%pi -- + -- +--------+ +-------+ -- |2%pi - 1 |%pi - 1 -- 8%pi |-------- - 4%pi |------- -- \| 2%pi \| %pi -- / -- 4 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in211:=integrate(acos(sin(2*z))*cos(z), z= 0..4*%pi/3) -- -- +-+ -- 13%pi\|3 + 36 -- -------------- -- 12 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in213a:=integrate(log(abs(1+1/(-z)^(1/3))), z= 0..1,"noPole") -- -- 3+---+2 3+---+ -- 3+---+2 3+---+ \|- 1 + 2\|- 1 + 1 3+---+2 3+---+ -- - log(\|- 1 + 2\|- 1 + 1) + log(---------------------) - \|- 1 + 2\|- 1 -- 3+---+2 -- \|- 1 -- ---------------------------------------------------------------------------- -- 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in216a:=integrate(1/(1/z-1)^(1/3), z= 0..1,"noPole") -- -- 2%pi -- ----- -- +-+ -- 3\|3 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2023a:=integrate((1-z)/(-1+z^(1/2)), z= 1..2,"noPole") -- -- +-+ -- - 4\|2 - 1 -- (33) ----------- -- 3 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2024a:=integrate(log(1-1/z)+csc(z-1), z= 0..1,"noPole") -- -- (32) - infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2032a:=integrate(acoth(z)/z^(1/2), z= 0..1,"noPole") -- -- - 2log(2) + %pi -- (30) --------------- -- 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2040a:=integrate(log(1-1/z^4)+cot(z), z= -1..1,"noPole") -- -- (24) log(16) + log(4) + %pi -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2050a:=integrate(-csc(z-1)-1/z^(1/3), z= -1..1,"noPole") -- -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2051a:=integrate((z^2+I*z-1)^(1/2)*z, z= -1..1,"noPole") -- -- 7 5 3 +---+ 8 7 6 -- (108I - 1776I - 7104I + 6912I)\|- I - 18I + 228I + 936I -- + -- 5 4 3 2 -- - 1104I + 2208I - 7488I - 7296I + 2304I -- * -- +-+ -- \|I -- + -- 8 7 6 5 4 3 2 -- - 18I - 228I + 936I + 1104I + 2208I + 7488I - 7296I -- + -- - 2304I -- * -- +---+ -- \|- I -- + -- 9 7 3 -- 3I - 744I + 11904I - 768I -- * -- +---+ 2 -- log((- 4I + 8)\|- I + I - 8I + 4) -- + -- 7 5 3 +---+ 8 7 6 -- (- 108I + 1776I + 7104I - 6912I)\|- I + 18I - 228I - 936I -- + -- 5 4 3 2 -- 1104I - 2208I + 7488I + 7296I - 2304I -- * -- +-+ -- \|I -- + -- 8 7 6 5 4 3 2 -- (18I + 228I - 936I - 1104I - 2208I - 7488I + 7296I + 2304I) -- * -- +---+ -- \|- I -- + -- 9 7 3 -- - 3I + 744I - 11904I + 768I -- * -- +-+ 2 -- log((- 4I - 8)\|I + I + 8I + 4) -- + -- 6 4 2 +---+ 8 7 6 5 -- (1728I - 10752I - 5120I )\|- I - 12I - 424I + 2736I + 6816I -- + -- 4 3 2 -- - 6208I + 1152I - 3840I - 512I -- * -- +-+ -- \|I -- + -- 8 7 6 5 4 3 2 +---+ -- (12I - 424I - 2736I + 6816I + 6208I + 1152I + 3840I - 512I)\|- I -- + -- 8 6 4 2 -- 144I - 6848I + 3840I + 3072I -- / -- 4 2 +---+ 5 4 3 2 -- (3456I - 70656I + 55296)\|- I - 576I + 7296I + 32256I - 64512I -- + -- - 58368I + 18432 -- * -- +-+ -- \|I -- + -- 5 4 3 2 +---+ 6 -- (- 576I - 7296I + 32256I + 64512I - 58368I - 18432)\|- I + 96I -- + -- 4 2 -- - 24192I + 96768I - 6144 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2053a:=integrate(atan(2*z-1), z= 0..infinity,"noPole") -- -- 4 3 2 -- - log(4infinity - 8infinity + 8infinity - 4infinity + 1) -- + -- 2infinity - 1 -- (- 4infinity + 2)atan(----------------------) - %pi -- 2 -- 2infinity - 2infinity -- / -- 8 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2054:=integrate(atan(1/z^(1/2))+1, z= -1..1) -- -- 4 3 2 -- - log(4infinity - 8infinity + 8infinity - 4infinity + 1) -- + -- 2infinity - 1 -- (- 4infinity + 2)atan(----------------------) - %pi -- 2 -- 2infinity - 2infinity -- / -- 8 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2056a:=integrate(z^(1/2)-acoth(1-z), z= 0..1,"noPole") -- -- - 3log(4) + 4 -- ------------- -- 6 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2058a:=integrate((z^2+I*z-3)^(1/2)+z, z= -1..1,"noPole") -- -- 4 2 +-------+ 5 4 3 2 -- (- 16I - 128I + 768)\|- I - 2 + 4I - 24I - 32I - 320I -- + -- - 960I - 384 -- * -- +-----+ -- \|I - 2 -- + -- 5 4 3 2 +-------+ 6 4 -- (4I + 24I - 32I + 320I - 960I + 384)\|- I - 2 - I + 60I -- + -- 2 -- 848I - 192 -- * -- +-------+ 2 -- log((- 4I + 8)\|- I - 2 + I - 8I - 4) -- + -- 4 2 +-------+ 5 4 3 2 -- (16I + 128I - 768)\|- I - 2 - 4I + 24I + 32I + 320I + 960I -- + -- 384 -- * -- +-----+ -- \|I - 2 -- + -- 5 4 3 2 +-------+ 6 4 -- (- 4I - 24I + 32I - 320I + 960I - 384)\|- I - 2 + I - 60I -- + -- 2 -- - 848I + 192 -- * -- +-----+ 2 -- log((- 4I - 8)\|I - 2 + I + 8I - 4) -- + -- 3 +-------+ 5 4 3 2 -- (- 256I + 1024I)\|- I - 2 + 4I + 72I - 288I - 1088I + 64I -- + -- 1152 -- * -- +-----+ -- \|I - 2 -- + -- 5 4 3 2 +-------+ 5 3 -- (- 4I + 72I + 288I - 1088I - 64I + 1152)\|- I - 2 - 32I + 768I -- + -- - 2560I -- / -- 2 +-------+ 3 2 +-----+ -- ((256I - 1024)\|- I - 2 - 64I + 384I + 1280I + 512)\|I - 2 -- + -- 3 2 +-------+ 4 2 -- (- 64I - 384I + 1280I - 512)\|- I - 2 + 16I - 1152I + 256 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2068a:=integrate(1/(I*z)^(1/2)-csch(z), z= 0..1,"noPole") -- -- - infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2071a:=integrate(1/(3+z)^3*acoth(z), z= -1..1,"noPole") -- -- - 3log(16) + 3log(4) - 2 -- ------------------------ -- 128 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2090a:=integrate(exp(z^(1/3))*(3+z)^9, z= -1..1,"noPole") -- -- 3+---+2 -- 13467752003249079711273325865856\|- 1 -- + -- 3+---+ -- - 27601768453337700619258203429120\|- 1 -- + -- 30944953633416008247597858726912 -- * -- 3+---+ -- \|- 1 -- %e -- + -- - 9746099248106233432776547720320%e -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2094a:=integrate(asinh(z)-acoth(z), z= -1..1,"noPole") -- -- +-+ +-+ -- log(2\|2 + 3) + log(- 2\|2 + 3) -- --------------------------------- -- 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2096a:=integrate(log(z)^2, z= %minusInfinity..%plusInfinity) -- -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2098a:=integrate(1/z^(1/3)-z^2/(z-1)^2, z= -1..1,"noPole") -- -- - infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2105a:=integrate(-1/(z^2-I*z+2)^(1/2)/z, z= 0..1,"noPole") -- -- - infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2106a:=integrate(acos(z)+acoth(1-z), z= 0..1,"noPole") -- -- log(4) + 2 -- ---------- -- 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2108a:=integrate((1-I/(1+I/z)^2)^(1/2), z= -1..1,"noPole") -- --[ -- +-----------+ +----------+ -- 2 | 2 3 2 | 2 -- (I \|I - 3I + 1 - I + I )\|I + I + 1 -- + -- +-----------+ -- 3 2 | 2 4 2 -- (- I - I )\|I - 3I + 1 + I - I -- * -- log -- 3 2 +-------+ 4 3 2 -- ((4I - 4I + 2I - 2)\|- I + 1 - 2I + 4I - 6I + 4I) -- * -- +----------+ -- | 2 -- \|I + I + 1 -- + -- 4 3 2 +-------+ 5 4 3 2 -- (- 4I + 2I - 2I + 4I)\|- I + 1 + 2I - 3I + 5I - 4I -- + -- 2I - 2 -- / -- +----------+ -- | 2 2 -- (2I + 2)\|I + I + 1 - 2I - 3I - 2 -- + -- +-----------+ -- +---+ +-------+ | 2 2 +---+ +-------+ -- (- I\|- I \|- I + 1 \|I - 3I + 1 + (I - I)\|- I \|- I + 1 ) -- * -- +----------+ -- | 2 -- \|I + I + 1 -- + -- +-----------+ -- 2 +---+ +-------+ | 2 3 +---+ +-------+ -- (I + I)\|- I \|- I + 1 \|I - 3I + 1 + (- I + I)\|- I \|- I + 1 -- * -- log -- +-----------+ -- 2 +---+ 3 2 | 2 -- ((4I - 10I + 4)\|- I + 2I - 10I + 10I - 2)\|I - 3I + 1 -- + -- 3 2 +---+ 4 3 2 -- (- 4I + 16I - 16I + 4)\|- I - 2I + 13I - 24I + 13I - 2 -- / -- +-----------+ -- 3 2 | 2 4 3 2 -- (2I - 6I + 6I - 2)\|I - 3I + 1 - 2I + 9I - 14I + 9I - 2 -- + -- +-----------+ -- +---+ +-------+ | 2 2 +---+ +-------+ -- (I\|- I \|- I + 1 \|I - 3I + 1 + (- I + I)\|- I \|- I + 1 ) -- * -- +----------+ -- | 2 -- \|I + I + 1 -- + -- +-----------+ -- 2 +---+ +-------+ | 2 3 +---+ +-------+ -- (- I - I)\|- I \|- I + 1 \|I - 3I + 1 + (I - I)\|- I \|- I + 1 -- * -- log -- +----------+ -- 2 +---+ 3 2 | 2 -- ((- 4I - 6I - 4)\|- I + 2I + 2I + 2I + 2)\|I + I + 1 -- + -- 3 2 +---+ 4 3 2 -- (4I + 8I + 8I + 4)\|- I - 2I - 3I - 4I - 3I - 2 -- / -- +----------+ -- 3 2 | 2 4 3 2 -- (2I + 6I + 6I + 2)\|I + I + 1 - 2I - 7I - 10I - 7I - 2 -- + -- +-----------+ +----------+ -- 2 | 2 3 2 | 2 -- (- I \|I - 3I + 1 + I - I )\|I + I + 1 -- + -- +-----------+ -- 3 2 | 2 4 2 -- (I + I )\|I - 3I + 1 - I + I -- * -- log -- 3 2 +-------+ 4 3 2 -- ((- 4I + 8I - 6I + 2)\|- I + 1 - 2I + 8I - 10I + 4I) -- * -- +-----------+ -- | 2 -- \|I - 3I + 1 -- + -- 4 3 2 +-------+ 5 4 3 2 -- (4I - 14I + 14I - 4I)\|- I + 1 + 2I - 11I + 21I - 20I -- + -- 10I - 2 -- / -- +-----------+ -- | 2 2 -- (2I - 2)\|I - 3I + 1 - 2I + 5I - 2 -- + -- +-----------+ +----------+ -- +-------+ | 2 +-------+ | 2 -- (- 4\|- I + 1 \|I - 3I + 1 + (6I - 4)\|- I + 1 )\|I + I + 1 -- + -- +-----------+ -- +-------+ | 2 2 +-------+ -- (2I + 4)\|- I + 1 \|I - 3I + 1 + (- 4I - 4I + 4)\|- I + 1 -- / -- +-----------+ +----------+ -- +-------+ | 2 +-------+ | 2 -- (2\|- I + 1 \|I - 3I + 1 + (- 2I + 2)\|- I + 1 )\|I + I + 1 -- + -- +-----------+ -- +-------+ | 2 2 +-------+ -- (- 2I - 2)\|- I + 1 \|I - 3I + 1 + (2I - 2)\|- I + 1 -- , -- -- +-----------+ -- +---+ +-----+ | 2 2 +---+ +-----+ -- (- I\|- I \|I - 1 \|I - 3I + 1 + (I - I)\|- I \|I - 1 ) -- * -- +----------+ -- | 2 -- \|I + I + 1 -- + -- +-----------+ -- 2 +---+ +-----+ | 2 3 +---+ +-----+ -- (I + I)\|- I \|I - 1 \|I - 3I + 1 + (- I + I)\|- I \|I - 1 -- * -- log -- +-----------+ -- 2 +---+ 3 2 | 2 -- ((4I - 10I + 4)\|- I + 2I - 10I + 10I - 2)\|I - 3I + 1 -- + -- 3 2 +---+ 4 3 2 -- (- 4I + 16I - 16I + 4)\|- I - 2I + 13I - 24I + 13I - 2 -- / -- +-----------+ -- 3 2 | 2 4 3 2 -- (2I - 6I + 6I - 2)\|I - 3I + 1 - 2I + 9I - 14I + 9I - 2 -- + -- +-----------+ -- +---+ +-----+ | 2 2 +---+ +-----+ -- (I\|- I \|I - 1 \|I - 3I + 1 + (- I + I)\|- I \|I - 1 ) -- * -- +----------+ -- | 2 -- \|I + I + 1 -- + -- +-----------+ -- 2 +---+ +-----+ | 2 3 +---+ +-----+ -- (- I - I)\|- I \|I - 1 \|I - 3I + 1 + (I - I)\|- I \|I - 1 -- * -- log -- +----------+ -- 2 +---+ 3 2 | 2 -- ((- 4I - 6I - 4)\|- I + 2I + 2I + 2I + 2)\|I + I + 1 -- + -- 3 2 +---+ 4 3 2 -- (4I + 8I + 8I + 4)\|- I - 2I - 3I - 4I - 3I - 2 -- / -- +----------+ -- 3 2 | 2 4 3 2 -- (2I + 6I + 6I + 2)\|I + I + 1 - 2I - 7I - 10I - 7I - 2 -- + -- +-----------+ +----------+ -- 2 | 2 3 2 | 2 -- (- 4I \|I - 3I + 1 + 4I - 4I )\|I + I + 1 -- + -- +-----------+ -- 3 2 | 2 4 2 -- (4I + 4I )\|I - 3I + 1 - 4I + 4I -- * -- +----------+ -- +-----+ | 2 +-----+ -- \|I - 1 \|I + I + 1 - I\|I - 1 -- atan(---------------------------------) -- I - 1 -- + -- +-----------+ +----------+ -- 2 | 2 3 2 | 2 -- (- 4I \|I - 3I + 1 + 4I - 4I )\|I + I + 1 -- + -- +-----------+ -- 3 2 | 2 4 2 -- (4I + 4I )\|I - 3I + 1 - 4I + 4I -- * -- +-----------+ -- +-----+ | 2 +-----+ -- \|I - 1 \|I - 3I + 1 - I\|I - 1 -- atan(----------------------------------) -- I - 1 -- + -- +-----------+ +----------+ -- +-----+ | 2 +-----+ | 2 -- (- 4\|I - 1 \|I - 3I + 1 + (6I - 4)\|I - 1 )\|I + I + 1 -- + -- +-----------+ -- +-----+ | 2 2 +-----+ -- (2I + 4)\|I - 1 \|I - 3I + 1 + (- 4I - 4I + 4)\|I - 1 -- / -- +-----------+ +----------+ -- +-----+ | 2 +-----+ | 2 -- (2\|I - 1 \|I - 3I + 1 + (- 2I + 2)\|I - 1 )\|I + I + 1 -- + -- +-----------+ -- +-----+ | 2 2 +-----+ -- (- 2I - 2)\|I - 1 \|I - 3I + 1 + (2I - 2)\|I - 1 -- , -- -- +-----------+ +----------+ -- 2 | 2 3 2 | 2 -- (I \|I - 3I + 1 - I + I )\|I + I + 1 -- + -- +-----------+ -- 3 2 | 2 4 2 -- (- I - I )\|I - 3I + 1 + I - I -- * -- log -- 3 2 +-------+ 4 3 2 -- ((4I - 4I + 2I - 2)\|- I + 1 - 2I + 4I - 6I + 4I) -- * -- +----------+ -- | 2 -- \|I + I + 1 -- + -- 4 3 2 +-------+ 5 4 3 2 -- (- 4I + 2I - 2I + 4I)\|- I + 1 + 2I - 3I + 5I - 4I -- + -- 2I - 2 -- / -- +----------+ -- | 2 2 -- (2I + 2)\|I + I + 1 - 2I - 3I - 2 -- + -- +-----------+ +----------+ -- 2 | 2 3 2 | 2 -- (- I \|I - 3I + 1 + I - I )\|I + I + 1 -- + -- +-----------+ -- 3 2 | 2 4 2 -- (I + I )\|I - 3I + 1 - I + I -- * -- log -- 3 2 +-------+ 4 3 2 -- ((- 4I + 8I - 6I + 2)\|- I + 1 - 2I + 8I - 10I + 4I) -- * -- +-----------+ -- | 2 -- \|I - 3I + 1 -- + -- 4 3 2 +-------+ 5 4 3 2 -- (4I - 14I + 14I - 4I)\|- I + 1 + 2I - 11I + 21I - 20I -- + -- 10I - 2 -- / -- +-----------+ -- | 2 2 -- (2I - 2)\|I - 3I + 1 - 2I + 5I - 2 -- + -- +-----------+ -- +-------+ +-+ | 2 2 +-------+ +-+ -- (- 4I\|- I + 1 \|I \|I - 3I + 1 + (4I - 4I)\|- I + 1 \|I ) -- * -- +----------+ -- | 2 -- \|I + I + 1 -- + -- +-----------+ -- 2 +-------+ +-+ | 2 3 +-------+ +-+ -- (4I + 4I)\|- I + 1 \|I \|I - 3I + 1 + (- 4I + 4I)\|- I + 1 \|I -- * -- +-+ -- \|I -- atan(----------------------) -- +-----------+ -- | 2 -- \|I - 3I + 1 - I + 1 -- + -- +-----------+ -- +-------+ +-+ | 2 2 +-------+ +-+ -- (- 4I\|- I + 1 \|I \|I - 3I + 1 + (4I - 4I)\|- I + 1 \|I ) -- * -- +----------+ -- | 2 -- \|I + I + 1 -- + -- +-----------+ -- 2 +-------+ +-+ | 2 3 +-------+ +-+ -- (4I + 4I)\|- I + 1 \|I \|I - 3I + 1 + (- 4I + 4I)\|- I + 1 \|I -- * -- +-+ -- \|I -- atan(---------------------) -- +----------+ -- | 2 -- \|I + I + 1 - I - 1 -- + -- +-----------+ +----------+ -- +-------+ | 2 +-------+ | 2 -- (- 4\|- I + 1 \|I - 3I + 1 + (6I - 4)\|- I + 1 )\|I + I + 1 -- + -- +-----------+ -- +-------+ | 2 2 +-------+ -- (2I + 4)\|- I + 1 \|I - 3I + 1 + (- 4I - 4I + 4)\|- I + 1 -- / -- +-----------+ +----------+ -- +-------+ | 2 +-------+ | 2 -- (2\|- I + 1 \|I - 3I + 1 + (- 2I + 2)\|- I + 1 )\|I + I + 1 -- + -- +-----------+ -- +-------+ | 2 2 +-------+ -- (- 2I - 2)\|- I + 1 \|I - 3I + 1 + (2I - 2)\|- I + 1 -- , -- -- +-----------+ +----------+ -- 2 | 2 3 2 | 2 -- (- 2I \|I - 3I + 1 + 2I - 2I )\|I + I + 1 -- + -- +-----------+ -- 3 2 | 2 4 2 -- (2I + 2I )\|I - 3I + 1 - 2I + 2I -- * -- +----------+ -- +-----+ | 2 +-----+ -- \|I - 1 \|I + I + 1 - I\|I - 1 -- atan(---------------------------------) -- I - 1 -- + -- +-----------+ +----------+ -- 2 | 2 3 2 | 2 -- (- 2I \|I - 3I + 1 + 2I - 2I )\|I + I + 1 -- + -- +-----------+ -- 3 2 | 2 4 2 -- (2I + 2I )\|I - 3I + 1 - 2I + 2I -- * -- +-----------+ -- +-----+ | 2 +-----+ -- \|I - 1 \|I - 3I + 1 - I\|I - 1 -- atan(----------------------------------) -- I - 1 -- + -- +-----------+ -- +-----+ +-+ | 2 2 +-----+ +-+ -- (- 2I\|I - 1 \|I \|I - 3I + 1 + (2I - 2I)\|I - 1 \|I ) -- * -- +----------+ -- | 2 -- \|I + I + 1 -- + -- +-----------+ -- 2 +-----+ +-+ | 2 3 +-----+ +-+ -- (2I + 2I)\|I - 1 \|I \|I - 3I + 1 + (- 2I + 2I)\|I - 1 \|I -- * -- +-+ -- \|I -- atan(----------------------) -- +-----------+ -- | 2 -- \|I - 3I + 1 - I + 1 -- + -- +-----------+ -- +-----+ +-+ | 2 2 +-----+ +-+ -- (- 2I\|I - 1 \|I \|I - 3I + 1 + (2I - 2I)\|I - 1 \|I ) -- * -- +----------+ -- | 2 -- \|I + I + 1 -- + -- +-----------+ -- 2 +-----+ +-+ | 2 3 +-----+ +-+ -- (2I + 2I)\|I - 1 \|I \|I - 3I + 1 + (- 2I + 2I)\|I - 1 \|I -- * -- +-+ -- \|I -- atan(---------------------) -- +----------+ -- | 2 -- \|I + I + 1 - I - 1 -- + -- +-----------+ +----------+ -- +-----+ | 2 +-----+ | 2 -- (- 2\|I - 1 \|I - 3I + 1 + (3I - 2)\|I - 1 )\|I + I + 1 -- + -- +-----------+ -- +-----+ | 2 2 +-----+ -- (I + 2)\|I - 1 \|I - 3I + 1 + (- 2I - 2I + 2)\|I - 1 -- / -- +-----------+ +----------+ -- +-----+ | 2 +-----+ | 2 -- (\|I - 1 \|I - 3I + 1 + (- I + 1)\|I - 1 )\|I + I + 1 -- + -- +-----------+ -- +-----+ | 2 2 +-----+ -- (- I - 1)\|I - 1 \|I - 3I + 1 + (I - 1)\|I - 1 -- ] -- Type: Union(f2: List OrderedCompletion Expression Integer,...) in2109a:=integrate((1+I*z)^(1/2)+cot(z-1), z= 0..1,"noPole") -- -- - infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2112a:=integrate(-cot(z-1)+log(1-1/z^4), z= -1..1,"noPole") -- -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2115a:=integrate(-z/(z-1)+log(1-z^(1/3)), z= -1..1,"noPole") -- -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2120a:=integrate(-z+1/(z^2+I*z-3)^(1/2), z= -1..1,"noPole") -- -- +-------+ 2 -- log((- 4I + 8)\|- I - 2 + I - 8I - 4) -- + -- +-----+ 2 -- - log((- 4I - 8)\|I - 2 + I + 8I - 4) -- / -- 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2124a:=integrate(-1/z-1/(I/(z+I))^(1/2), z= -1..0,"noPole") -- -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in25:=integrate(cos(z), z= %i..a) -- -- sin(a) - sin(I) -- Type: Union(f1: OrderedCompletion Expression Integer,...) in25a:=integrate(cos(z), z= %i..a) -- -- sin(a) - sin(%i) -- Type: Union(f1: OrderedCompletion Expression Complex Integer,...) in25b:=integrate(exp(I*z), z= %i..%i*infinity) -- -- 2 2 -- I infinity I -- %e - %e -- ------------------- -- I -- Type: Union(f1: OrderedCompletion Expression Integer,...) in25c:=integrate(exp(%i*z), z= %i..I*infinity) -- -- %i I infinity -- - %i %e %e + %i -- ---------------------------- -- %e -- Type: Union(f1: OrderedCompletion Expression Complex Integer,...) in28a:=integrate(1/z, z=1..z,"noPole") -- -- 2 -- log(z ) -- ------- -- 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in30:=integrate(sin(3*asin(1/(1+z^2))), z= 0..%plusInfinity) -- -- 3%pi -- ---- -- 4 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in32:=integrate(exp(-z), z= 0..%plusInfinity) -- -- 1 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in34a:=integrate(1/(sin(z)-1/2), z= 0..1,"noPole") -- -- log -- 2 2 -- - 12sin(1) + (42cos(1) + 48)sin(1) - 36cos(1) - 84cos(1) -- + -- - 48 -- * -- +-+ -- \|3 -- + -- 2 2 -- 21sin(1) + (- 72cos(1) - 84)sin(1) + 63cos(1) + 144cos(1) + 84 -- / -- 2 -- 4sin(1) - 4sin(1) + 1 -- + -- +-+ -- - log(- 168\|3 + 291) -- / -- +-+ -- \|3 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in37:=integrate(atan(tan(1/z)), z= 0..1) -- -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in40:=integrate(atan(tan(z)), z= 0..%plusInfinity) -- -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2157a:=integrate(acoth(z)-1/(1+z^(1/2)), z= 0..1,"noPole") -- -- log(4) + 10log(2) - 8 -- --------------------- -- 4 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2158a:=integrate(2*acoth(1-(1-z)^(1/2)), z= 0..1,"noPole") -- -- 2log(4) - 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2168a:=integrate(-csch(z-1)-(1+I*z)^(1/2), z= 0..1,"noPole") -- -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2179a:=integrate((z^3-I*(1-z^4)^(1/2))^4, z= -1..1,"noPole") -- -- 4 2 -- 64064I + 28080I + 6930 -- (104) ------------------------ -- 45045 -- Type: Union(f1: OrderedCompletion Expression Integer,...) -- in2185a:=integrate(csch(z)+(z^2-I*z+1)^(1/2), z= 0..1,"noPole") -- -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2195a:=integrate(1-acoth(1-(1-z)^(1/2)), z= -1..1,"noPole") -- -- +-+ +-+ +-+ +-+ -- 2log(\|2 ) - log(- 2\|2 + 3) + 3log(- 4\|2 + 6) + 4\|2 - 4log(4) + 8 -- ----------------------------------------------------------------------- -- 4 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2201a:=integrate(acoth(z)+%pi-asec(z-1), z= 0..1,"noPole") -- -- +-+ -- - %pi\|2 + log(4) + 2%pi -- ------------------------- -- 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in221:=integrate(log(z+sqrt(z^2-1)), z) -- -- +------+ +------+ +------+ -- | 2 2 | 2 | 2 2 -- (z\|z - 1 - z )log(\|z - 1 + z) + z\|z - 1 - z + 1 -- --------------------------------------------------------- -- +------+ -- | 2 -- \|z - 1 - z -- Type: Union(Expression Integer,...) in227a:=integrate(atan(sin(z))+atan(1/(sin(z))), z= 0..1,"noPole") -- -- %pi -- - --- -- 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in237a:=integrate(sin(z)*(1-cos(z)/sqrt(1-sin(z)^2))^2, z= 0..1,"noPole") -- -- - 4cos(1) + 4 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2221:=integrate((z-I)*(-1+1/(z-I)), z= 0..%plusInfinity) -- -- - infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2243a:=integrate(-1/sinh(z-1)+1/(I*z)^(1/2), z= 0..1,"noPole") -- -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2247a:=integrate(1/(z^2-I*z+2)^(1/2)+csc(z), z= 0..1,"noPole") -- -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2254a:=integrate(cosh(z^(1/2))-acoth(1-z), z= 0..1,"noPole") -- -- - %e log(4) + 4%e - 4 -- --------------------- -- 2%e -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2270a:=integrate(log(z)*log(1/z)*(I*z)^(1/3), z= -1..1,"noPole") -- -- 3+-+ 3+---+ -- - 27\|I - 27\|- I -- ------------------- -- 32 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2274a:=integrate(acoth(1-z)-acosh(1/z), z= -1..1,"noPole") -- -- 3log(9) - 4%pi -- -------------- -- 4 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2275a:=integrate((z^2+I*z-3)^(1/2)*(3+z^2), z= -1..1,"noPole") -- -- 10 8 6 4 2 -- - 960I + 49920I + 1320960I + 3563520I - 40550400I -- + -- 8847360 -- * -- +-------+ -- \|- I - 2 -- + -- 11 10 9 8 7 6 -- 120I - 2640I - 23520I + 10560I - 318720I + 1359360I -- + -- 5 4 3 2 -- 3056640I + 9922560I + 36034560I - 2396160I - 40919040I -- + -- 15482880 -- * -- +-----+ -- \|I - 2 -- + -- 11 10 9 8 7 6 -- 120I + 2640I - 23520I - 10560I - 318720I - 1359360I -- + -- 5 4 3 2 -- 3056640I - 9922560I + 36034560I + 2396160I - 40919040I -- + -- - 15482880 -- * -- +-------+ -- \|- I - 2 -- + -- 12 10 8 6 4 2 -- - 15I + 12360I + 67440I - 3283200I - 21131520I + 73451520I -- + -- - 27095040 -- * -- +-------+ 2 -- log((- 4I + 8)\|- I - 2 + I - 8I - 4) -- + -- 10 8 6 4 2 -- 960I - 49920I - 1320960I - 3563520I + 40550400I -- + -- - 8847360 -- * -- +-------+ -- \|- I - 2 -- + -- 11 10 9 8 7 6 -- - 120I + 2640I + 23520I - 10560I + 318720I - 1359360I -- + -- 5 4 3 2 -- - 3056640I - 9922560I - 36034560I + 2396160I + 40919040I -- + -- - 15482880 -- * -- +-----+ -- \|I - 2 -- + -- 11 10 9 8 7 6 -- - 120I - 2640I + 23520I + 10560I + 318720I + 1359360I -- + -- 5 4 3 2 -- - 3056640I + 9922560I - 36034560I - 2396160I + 40919040I -- + -- 15482880 -- * -- +-------+ -- \|- I - 2 -- + -- 12 10 8 6 4 2 -- 15I - 12360I - 67440I + 3283200I + 21131520I - 73451520I -- + -- 27095040 -- * -- +-----+ 2 -- log((- 4I - 8)\|I - 2 + I + 8I - 4) -- + -- 9 5 3 +-------+ 11 -- (- 20480I + 17170432I - 48234496I + 57671680I)\|- I - 2 + 60I -- + -- 10 9 8 7 6 5 -- 3800I - 39408I - 172896I - 790144I - 6873344I + 13455872I -- + -- 4 3 2 -- 53588992I - 16978944I - 85084160I + 9687040I + 21897216 -- * -- +-----+ -- \|I - 2 -- + -- 11 10 9 8 7 6 -- - 60I + 3800I + 39408I - 172896I + 790144I - 6873344I -- + -- 5 4 3 2 -- - 13455872I + 53588992I + 16978944I - 85084160I - 9687040I -- + -- 21897216 -- * -- +-------+ -- \|- I - 2 -- + -- 11 9 7 5 3 -- - 960I + 133888I + 3352576I - 44081152I + 129318912I - 59834368I -- / -- 6 4 2 +-------+ 7 -- (49152I - 3735552I + 14942208I - 3145728)\|- I - 2 - 6144I -- + -- 6 5 4 3 2 -- 135168I + 1351680I - 3784704I - 15237120I + 1769472I + 14548992I -- + -- - 5505024 -- * -- +-----+ -- \|I - 2 -- + -- 7 6 5 4 3 2 -- - 6144I - 135168I + 1351680I + 3784704I - 15237120I - 1769472I -- + -- 14548992I + 5505024 -- * -- +-------+ -- \|- I - 2 -- + -- 8 6 4 2 -- 768I - 651264I + 12066816I - 27721728I + 9633792 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2276a:=integrate((1-tanh(log(1+z^(1/3))))^5, z= -1..1,"noPole") -- -- 3+---+2 3+---+ 3+---+ -- (- 918750\|- 1 + 1200000\|- 1 + 2100000)atan(\|- 1 + 1) -- + -- 3+---+2 3+---+ -- (918750atan(2) - 466984)\|- 1 + (- 1200000atan(2) - 364526)\|- 1 -- + -- - 2100000atan(2) + 96142 -- / -- 3+---+2 3+---+ -- 30625\|- 1 - 40000\|- 1 - 70000 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2278a:=integrate(acoth(1-z)+log(abs(z-1)/z), z= 0..1,"noPole") -- -- log(4) -- (120) ------ -- 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2279a:=integrate(acoth(1/(z^2-z+1)^(1/2)), z= -1..1,"noPole") -- -- +-+ -- +-+ +-+ +-+ - \|3 - 2 -- 2log(12\|3 + 21) + log(6\|3 + 12) - log(2\|3 + 4) + log(----------) -- +-+ -- \|3 - 2 -- + -- log(16) - 2log(4) -- / -- 4 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2307a:=integrate(tan(z)-1/(z^2+I*z-3)^(1/2), z= -1..1,"noPole") -- -- +-------+ 2 -- - log((- 4I + 8)\|- I - 2 + I - 8I - 4) -- + -- +-----+ 2 -- log((- 4I - 8)\|I - 2 + I + 8I - 4) -- / -- 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2311a:=integrate(-1/sinh(z-1)+1/(I*z)^(1/2), z= 0..%pi,"noPole") -- -- %pi - 1 2 %pi - 1 -- I log((%e ) + 2%e + 1) -- + -- 2 -- %pi - 1 2 %pi - 1 +-----+ %e + 2%e + 1 -- - I log((%e ) - 2%e + 1) + 4\|I %pi - I log(-------------) -- 2 -- %e -- + -- 2 -- %e - 2%e + 1 -- I log(-------------) -- 2 -- %e -- / -- 2I -- Type: Union(f1: OrderedCompletion Expression Integer,...) ------------------------------------------------------ in2312:=integrate(sin(z)-1/(z^2+I*z-1)^(1/2), z= -1..1) -- -- potentialPole -- in2312a:=integrate(sin(z)-1/(z^2+I*z-1)^(1/2), z= -1..1,"noPole") -- -- +---+ 2 +-+ 2 -- - log((- 4I + 8)\|- I + I - 8I + 4) + log((- 4I - 8)\|I + I + 8I + 4) -- ------------------------------------------------------------------------- -- 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2324a:=integrate(cosh(z^(1/2)-1)+acoth(1-z), z= 0..1,"noPole") -- -- 2 -- %e log(4) + 2%e - 4%e + 2 -- -------------------------- -- 2%e -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2330a:=integrate(exp(-z)+1/(z^2+I*z-1)^(1/2), z= -1..1,"noPole") -- -- +---+ 2 -- %e log((- 4I + 8)\|- I + I - 8I + 4) -- + -- +-+ 2 2 -- - %e log((- 4I - 8)\|I + I + 8I + 4) + 2%e - 2 -- / -- 2%e -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2332a:=integrate(acoth(z^(1/2))*(1-z^(1/2)), z= 0..1,"noPole") -- -- log(16) - log(4) - 10log(2) + 8 -- ------------------------------- -- 12 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2333a:=integrate(acoth(z)+1/(z^2+z+2)^(1/2), z= 0..1,"noPole") -- -- +-+ -- log(- 4\|2 + 9) + log(4) -- ------------------------- -- 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2340a:=integrate(exp(I*(I*z)^(1/2))+cot(z-1), z= -1..1,"noPole") -- -- - infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2360a:=integrate(1/(1-I*z^2)^(1/2)-csch(z-1), z= -1..1,"noPole") -- -- [ + infinity, + infinity] -- Type: Union(f2: List OrderedCompletion Expression Integer,...) in2367a:=integrate(log(1-z^2)-1/(I/(z-I))^(1/2), z= -1..1,"noPole") -- -- 4 4 1 -- 3log(-----------) + 3log(-----------) - 3log(-----------) -- 2 2 2 -- I - 2I + 1 I + 2I + 1 I - 2I + 1 -- + -- 1 -- - 3log(-----------) + 6log(4) - 24 -- 2 -- I + 2I + 1 -- * -- +-------+ -- | I -- |- ----- -- \| I - 1 -- + -- 4I - 4 -- * -- +-------+ -- | I -- |- ----- -- \| I + 1 -- + -- +-------+ -- | I -- (- 4I - 4) |- ----- -- \| I - 1 -- / -- +-------+ +-------+ -- | I | I -- 6 |- ----- |- ----- -- \| I - 1 \| I + 1 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2375a:=integrate(acoth(1-z^(1/2))+1/z^(1/3), z= 0..1,"noPole") -- -- 2log(4) + 1 -- ----------- -- 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2376a:=integrate(log(1-z^(1/3)-z^(2/3)), z= 0..infinity,"noPole") -- -- +-+ -- 3\|5 -- * -- log -- +-+ 3+--------+2 -- (- 12\|5 - 36)\|infinity -- + -- +-+ 3+--------+ +-+ -- (- 16\|5 - 4infinity - 32)\|infinity + (- 8infinity - 6)\|5 -- + -- - 8infinity - 14 -- / -- 3+--------+2 3+--------+ -- \|infinity + (- infinity + 2)\|infinity - 2infinity - 1 -- + -- (3infinity + 6) -- * -- 3+--------+2 3+--------+ -- log(- \|infinity + (infinity - 2)\|infinity + 2infinity + 1) -- + -- 3+--------+2 3+--------+ +-+ +-+ -- 3\|infinity - 18\|infinity - 3\|5 log(6\|5 + 14) - 4infinity -- / -- 6 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2378a:=integrate((z^2+I*z-3)^(1/2)-tanh(z-1), z= -1..1,"noPole") -- -- 4 2 +-------+ 5 4 3 2 -- (- 16I - 128I + 768)\|- I - 2 + 4I - 24I - 32I - 320I -- + -- - 960I - 384 -- * -- +-----+ -- \|I - 2 -- + -- 5 4 3 2 +-------+ 6 4 -- (4I + 24I - 32I + 320I - 960I + 384)\|- I - 2 - I + 60I -- + -- 2 -- 848I - 192 -- * -- +-------+ 2 -- log((- 4I + 8)\|- I - 2 + I - 8I - 4) -- + -- 4 2 +-------+ 5 4 3 2 -- (16I + 128I - 768)\|- I - 2 - 4I + 24I + 32I + 320I + 960I -- + -- 384 -- * -- +-----+ -- \|I - 2 -- + -- 5 4 3 2 +-------+ 6 4 -- (- 4I - 24I + 32I - 320I + 960I - 384)\|- I - 2 + I - 60I -- + -- 2 -- - 848I + 192 -- * -- +-----+ 2 -- log((- 4I - 8)\|I - 2 + I + 8I - 4) -- + -- 2 4 2 2 -- 2 (%e ) + 2(%e ) + 1 2 -- (128I - 512)log(--------------------) + (- 128I + 512)log(4) -- 2 4 -- (%e ) -- + -- 3 2 -- - 256I + 512I + 1024I - 2048 -- * -- +-------+ -- \|- I - 2 -- + -- 2 4 2 2 -- 3 2 (%e ) + 2(%e ) + 1 -- (- 32I + 192I + 640I + 256)log(--------------------) -- 2 4 -- (%e ) -- + -- 3 2 5 4 3 2 -- (32I - 192I - 640I - 256)log(4) + 4I + 72I - 416I - 320I -- + -- 2624I + 2176 -- * -- +-----+ -- \|I - 2 -- + -- 2 4 2 2 -- 3 2 (%e ) + 2(%e ) + 1 -- (- 32I - 192I + 640I - 256)log(--------------------) -- 2 4 -- (%e ) -- + -- 3 2 5 4 3 2 -- (32I + 192I - 640I + 256)log(4) - 4I + 72I + 160I - 1856I -- + -- 2496I + 128 -- * -- +-------+ -- \|- I - 2 -- + -- 2 4 2 2 -- 4 2 (%e ) + 2(%e ) + 1 -- (8I - 576I + 128)log(--------------------) -- 2 4 -- (%e ) -- + -- 4 2 5 4 3 2 -- (- 8I + 576I - 128)log(4) - 32I + 32I + 768I - 2304I - 2560I + 512 -- / -- 2 +-------+ 3 2 +-----+ -- ((256I - 1024)\|- I - 2 - 64I + 384I + 1280I + 512)\|I - 2 -- + -- 3 2 +-------+ 4 2 -- (- 64I - 384I + 1280I - 512)\|- I - 2 + 16I - 1152I + 256 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2386a:=integrate(acoth(1-z)-(z^2-z+2)^(1/2), z= 0..1,"noPole") -- -- +-+ +-+ +-+ -- - 7log(4\|2 + 9) + 7log(- 4\|2 + 9) - 8\|2 + 8log(4) -- ------------------------------------------------------- -- 16 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2390a:=integrate((z^2-I*z-2)^(1/2)+1/sec(z-1), z= -1..1,"noPole") -- -- 8 6 4 2 +-------+ 9 8 -- (- 64I + 3840I + 18432I - 131072I )\|- I - 1 - 8I + 176I -- + -- 7 6 5 4 3 2 -- 1472I - 3456I - 1536I - 33792I - 102400I + 40960I + 65536I -- * -- +-----+ -- \|I - 1 -- + -- 9 8 7 6 5 4 3 -- - 8I - 176I + 1472I + 3456I - 1536I + 33792I - 102400I -- + -- 2 -- - 40960I + 65536I -- * -- +-------+ -- \|- I - 1 -- + -- 10 8 6 4 2 -- - I + 792I - 6016I - 84992I + 110592I - 32768 -- * -- +-----+ 2 -- log((4I + 8)\|I - 1 + I + 8I) -- + -- 8 6 4 2 +-------+ 9 8 -- (64I - 3840I - 18432I + 131072I )\|- I - 1 + 8I - 176I -- + -- 7 6 5 4 3 2 -- - 1472I + 3456I + 1536I + 33792I + 102400I - 40960I - 65536I -- * -- +-----+ -- \|I - 1 -- + -- 9 8 7 6 5 4 3 -- 8I + 176I - 1472I - 3456I + 1536I - 33792I + 102400I -- + -- 2 -- 40960I - 65536I -- * -- +-------+ -- \|- I - 1 -- + -- 10 8 6 4 2 -- I - 792I + 6016I + 84992I - 110592I + 32768 -- * -- +-------+ 2 -- log((4I - 8)\|- I - 1 + I - 8I) -- + -- 6 4 2 7 5 3 -- (1024I - 69632I + 262144I )sin(2) + 1536I - 63488I + 262144I -- + -- - 131072I -- * -- +-------+ -- \|- I - 1 -- + -- 7 6 5 4 3 2 -- (128I - 2816I - 24576I + 77824I + 221184I - 81920I - 131072I) -- * -- sin(2) -- + -- 9 8 7 6 5 4 3 -- 4I + 264I - 3456I - 24320I + 67072I + 199680I - 122880I -- + -- 2 -- - 245760I + 16384I + 32768 -- * -- +-----+ -- \|I - 1 -- + -- 7 6 5 4 3 2 -- (128I + 2816I - 24576I - 77824I + 221184I + 81920I - 131072I) -- * -- sin(2) -- + -- 9 8 7 6 5 4 3 -- - 4I + 264I + 3456I - 24320I - 67072I + 199680I + 122880I -- + -- 2 -- - 245760I - 16384I + 32768 -- * -- +-------+ -- \|- I - 1 -- + -- 8 6 4 2 9 7 -- (16I - 12800I + 198656I - 229376I + 65536)sin(2) + 64I - 13824I -- + -- 5 3 -- 174080I - 327680I + 131072I -- / -- 6 4 2 +-------+ 7 6 5 -- (1024I - 69632I + 262144I )\|- I - 1 + 128I - 2816I - 24576I -- + -- 4 3 2 -- 77824I + 221184I - 81920I - 131072I -- * -- +-----+ -- \|I - 1 -- + -- 7 6 5 4 3 2 -- (128I + 2816I - 24576I - 77824I + 221184I + 81920I - 131072I) -- * -- +-------+ -- \|- I - 1 -- + -- 8 6 4 2 -- 16I - 12800I + 198656I - 229376I + 65536 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2392a:=integrate(1/sec(z-1)+acoth(1-z^(1/2)), z= 0..1,"noPole") -- -- sin(1) + log(4) - 1 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2404a:=integrate(1/(1+I*z^2)^(1/2)+acoth(z), z= -1..1,"noPole") -- -- [ -- - -- log -- 2 +-+ 2 +-----+ 2 +-+ 3 -- ((2I + 4I)\|I + 4I + 2I)\|I + 1 + (- 4I - 4I)\|I - 2I -- + -- 2 -- - 5I - 2I -- / -- +-----+ -- 2\|I + 1 - I - 2 -- + -- log -- 2 +-+ 2 +-----+ 2 +-+ 3 -- ((- 2I - 4I)\|I + 4I + 2I)\|I + 1 + (4I + 4I)\|I - 2I -- + -- 2 -- - 5I - 2I -- / -- +-----+ -- 2\|I + 1 - I - 2 -- / -- +-+ -- 2\|I -- , -- +---+ +-----+ +---+ -- \|- I \|I + 1 - \|- I -- 4atan(-----------------------) -- I -- ------------------------------] -- +---+ -- \|- I -- Type: Union(f2: List OrderedCompletion Expression Integer,...) in2409a:=integrate(tan(z)+1/(I/(z+I))^(1/2), z= 0..1/2*%pi,"noPole") -- -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in248a:=integrate(log(z^I)^2, z= 0..1,"noPole") -- -- 2 -- 2I -- Type: Union(f1: OrderedCompletion Expression Integer,...) -- in248b:=integrate(log(z^%i)^2, z= 0..1,"noPole") -- -- - 2 -- Type: Union(f1: OrderedCompletion Expression Complex Integer,...) in249a:=integrate((sin(z)/(cos(z)-1))^(1/3), z= 0..%pi,"noPole") -- -- 3+-+ 3+-+ +-+ -- 3log(32\|2 ) - 12log(2\|2 ) - 4%pi\|3 -- -------------------------------------- -- 24 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in251a:=integrate((-1)^z*exp(-z)*sin(z), z= 0..%plusInfinity,"noPole") -- -- 2 -- - %pi + 2 -- ---------- -- 4 -- %pi + 4 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2434a:=integrate(acoth(z^(1/2))+log(abs(z-1)), z= 0..1,"noPole") -- -- log(16) + log(4) - 6log(2) -- -------------------------- -- 4 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2443a:=integrate(sech(z)+log(abs(1-1/z^(1/3))), z= -1..1,"noPole") -- -- 3+---+2 3+---+ -- 3+---+2 3+---+ \|- 1 - 2\|- 1 + 1 -- log(\|- 1 - 2\|- 1 + 1) + log(---------------------) + 4atan(%e) -- 3+---+2 -- \|- 1 -- + -- 1 3+---+2 3+---+ -- - 4atan(--) + \|- 1 + 2\|- 1 - 3 -- %e -- / -- 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2462a:=integrate(log((1+(1-z)^(1/2))/z)+csch(z), z= -1..0,"noPole") -- -- - infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2469a:=integrate(1/(2+z)^2+1/(z^2-I*z-2)^(1/2), z= -1..1,"noPole") -- -- +-----+ 2 +-------+ 2 -- 3log((4I + 8)\|I - 1 + I + 8I) - 3log((4I - 8)\|- I - 1 + I - 8I) + 4 -- ------------------------------------------------------------------------- -- 6 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2484a:=integrate(log(1-z^2)+sinh(z^(1/2)), z= 0..%plusInfinity,"noPole") -- -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2485a:=integrate(log(1-z^(1/2))-acoth(z^(1/2)), z= 0..1,"noPole") -- -- - log(16) + log(4) + 2log(2) - 10 -- --------------------------------- -- 4 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2521a:=integrate(acoth(z^(1/2))+cos(z^(1/2)-1), z= 0..1,"noPole") -- -- - 2cos(1) + 3 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2524a:=integrate(log(abs(1+1/z^(1/3)))+log(1+1/z), z= -1..0,"noPole") -- -- - infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2527a:=integrate(1/(1+I*z^(1/3))+cosh(z), z= %minusInfinity..0,"noPole") -- -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2533a:=integrate(log(abs(1-1/z^(1/3)))-log(1-1/z), z= -1..0,"noPole") -- 3+---+2 3+---+ -- 3+---+2 3+---+ \|- 1 - 2\|- 1 + 1 3+---+2 -- - log(3\|- 1 + \|- 1 - 1) + log(---------------------) + \|- 1 -- 3+---+2 -- \|- 1 -- + -- 3+---+ -- 2\|- 1 - log(4) -- / -- 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2566a:=integrate(log(1+(1-z)^(1/2))+acoth(1-z), z= -1..1,"noPole") -- -- +-+ +-+ -- 4log(\|2 + 1) + 4\|2 + 3log(9) - 4 -- ------------------------------------ -- 4 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2567a:=integrate(1/(I*z)^(1/3)*log(abs(z-1)), z= 0..1/2*%pi,"noPole") -- -- 3+---+3+-----+2 3+-+3+---+2 3+-----+ 2 3+-+2 -- 3+-+2 - I\|- I \|I %pi - 2I\|2 \|- I \|I %pi + I \|2 -- 6I \|2 log(----------------------------------------------------) -- 3+-+2 -- \|2 -- + -- - -- 3+-+2 -- 3I \|2 -- * -- log -- 3+---+3+-----+2 3+-+3+---+2 3+-----+ -- - 6I\|- I \|I %pi + (I %pi + 4I)\|2 \|- I \|I %pi -- + -- 2 2 3+-+2 -- (2I %pi + 2I )\|2 -- / -- 3+-+2 -- 2\|2 -- + -- 3+---+2 3+-----+ 3+-+ -- 3+-+2 +-+ 2\|- I \|I %pi + I\|2 -- 12I \|2 \|3 atan(------------------------) -- 3+-+ +-+ -- I\|2 \|3 -- + -- 2 -- %pi - 4%pi + 4 3+---+3+-----+2 3+-+2 2 -- (6log(---------------) - 18)\|- I \|I %pi - 3I \|2 log(I ) -- 4 -- + -- 3+-+2 +-+ -- - 2I %pi \|2 \|3 -- / -- 3+-+2 3+---+ -- 8I \|2 \|- I -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2586a:=integrate(acoth(z^(1/2))+atan(z^(1/2)), z= 0..1,"noPole") -- -- log(16) - log(4) - 2log(2) + 2%pi -- --------------------------------- -- 4 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2591a:=integrate(log(z)/(1-z^(1/2))^3-log(z)*log(-z), z= 0..1,"noPole") -- -- - infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2597a:=integrate((1+I/z)^(1/2)-log(1-1/z^2), z= 0..%plusInfinity,"noPole") -- -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2598a:=integrate(exp(-z^(1/2))+acoth(1-z^(1/2)), z= 0..1,"noPole") -- -- %e log(4) + %e - 4 -- (105) ------------------ -- %e -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2604a:=integrate(acoth(1-z^(1/2))+log(1+z^(1/3)), z= 1..2,"noPole") -- -- 6+-+2 6+-+3 6+-+3 6+-+4 -- 18log(\|2 + 1) + 3log(- 2\|2 + 3) - 6log(- 4\|2 + 6) + 3\|2 -- + -- 6+-+3 6+-+2 -- - 6\|2 - 6\|2 - 12log(2) + 7 -- / -- 6 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in271a:=integrate(1/sqrt((z^2-1)*(z^2-1)), z= 2..%plusInfinity,"noPole") -- -- log(9) -- (5) ------ -- 4 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in275c:=integrate(sqrt(z), z= -%i..%i,"noPole") -- -- +-+ +---+ -- 2I\|I + 2I\|- I -- (11) ----------------- -- 3 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in275a:=integrate(1/(1+z), z= -%i..%i,"noPole") -- -- 2 2 -- log(I + 2I + 1) - log(I - 2I + 1) -- (13) ----------------------------------- -- 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in275b:=integrate(1/(1+z), z= -%i..%i,"noPole") -- -- log(2%i) - log(- 2%i) -- (21) --------------------- -- 2 -- Type: Union(f1: OrderedCompletion Expression Complex Integer,...) in276a:=integrate(log(1-z^(1/3)-z^(2/3)), z= 0..sqrt(5)-2,"noPole") -- -- +-+ -- 3\|5 -- * -- log -- +--------+2 +--------+ -- +-+ 3| +-+ +-+ 3| +-+ +-+ -- (- 12\|5 - 36)\|\|5 - 2 + (- 20\|5 - 24)\|\|5 - 2 + 2\|5 -- + -- - 38 -- / -- +--------+2 +--------+ -- 3| +-+ +-+ 3| +-+ +-+ -- \|\|5 - 2 + (- \|5 + 4)\|\|5 - 2 - 2\|5 + 3 -- + -- +--------+2 +--------+ -- +-+ 3| +-+ +-+ 3| +-+ +-+ -- 3\|5 log(- \|\|5 - 2 + (\|5 - 4)\|\|5 - 2 + 2\|5 - 3) -- + -- +--------+2 +--------+ -- 3| +-+ 3| +-+ +-+ +-+ +-+ -- 3\|\|5 - 2 - 18\|\|5 - 2 - 3\|5 log(6\|5 + 14) - 4\|5 + 8 -- / -- 6 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2634a:=integrate(1/(z^2+I*z-1)^(1/2)+log(abs(z-1)), z= -1..1,"noPole") -- -- +---+ 2 +-+ 2 -- log((- 4I + 8)\|- I + I - 8I + 4) - log((- 4I - 8)\|I + I + 8I + 4) -- + -- 2log(4) - 4 -- / -- 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2656a:=integrate(acoth(1-(1-z)^(1/2))-log(1-1/z), z= -1..1,"noPole") -- -- +-+ +-+ +-+ +-+ -- - 10log(\|2 ) + log(- 2\|2 + 3) - 3log(- 4\|2 + 6) - 4\|2 + 2log(4) -- ---------------------------------------------------------------------- -- 4 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2676a:=integrate(acoth(1-(1-z)^(1/2))-log(1-1/z), z= -1..1,"noPole") -- -- +-+ +-+ +-+ +-+ -- - 10log(\|2 ) + log(- 2\|2 + 3) - 3log(- 4\|2 + 6) - 4\|2 + 2log(4) -- ---------------------------------------------------------------------- -- 4 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2664aa:=integrate(atanh(1/z)+(1+z^2)^(1/2), z= 0..%plusInfinity,"noPole") -- -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2681a:=integrate((z^2-I*z-3)^(1/2)+%pi-acot(z-1), z= -1..1,"noPole") -- -- 4 2 +-------+ 5 4 3 2 -- (- 16I - 128I + 768)\|- I - 2 - 4I + 24I + 32I + 320I -- + -- 960I + 384 -- * -- +-----+ -- \|I - 2 -- + -- 5 4 3 2 +-------+ 6 4 -- (- 4I - 24I + 32I - 320I + 960I - 384)\|- I - 2 - I + 60I -- + -- 2 -- 848I - 192 -- * -- +-----+ 2 -- log((4I + 8)\|I - 2 + I + 8I - 4) -- + -- 4 2 +-------+ 5 4 3 2 -- (16I + 128I - 768)\|- I - 2 + 4I - 24I - 32I - 320I - 960I -- + -- - 384 -- * -- +-----+ -- \|I - 2 -- + -- 5 4 3 2 +-------+ 6 4 -- (4I + 24I - 32I + 320I - 960I + 384)\|- I - 2 + I - 60I -- + -- 2 -- - 848I + 192 -- * -- +-------+ 2 -- log((4I - 8)\|- I - 2 + I - 8I - 4) -- + -- 2 2 4 2 -- (64I - 256)log(25) + (256I - 1024)atan(-) + (512I - 2048)%pi -- 3 -- + -- 3 -- 256I - 1024I -- * -- +-------+ -- \|- I - 2 -- + -- 3 2 -- (16I - 96I - 320I - 128)log(25) -- + -- 3 2 4 -- (64I - 384I - 1280I - 512)atan(-) -- 3 -- + -- 3 2 5 4 3 2 -- (128I - 768I - 2560I - 1024)%pi + 4I + 72I - 288I - 1088I + 64I -- + -- 1152 -- * -- +-----+ -- \|I - 2 -- + -- 3 2 -- (16I + 96I - 320I + 128)log(25) -- + -- 3 2 4 -- (64I + 384I - 1280I + 512)atan(-) -- 3 -- + -- 3 2 5 4 3 2 -- (128I + 768I - 2560I + 1024)%pi - 4I + 72I + 288I - 1088I - 64I -- + -- 1152 -- * -- +-------+ -- \|- I - 2 -- + -- 4 2 4 2 4 -- (4I - 288I + 64)log(25) + (16I - 1152I + 256)atan(-) -- 3 -- + -- 4 2 5 3 -- (32I - 2304I + 512)%pi + 32I - 768I + 2560I -- / -- 2 +-------+ 3 2 +-----+ -- ((256I - 1024)\|- I - 2 + 64I - 384I - 1280I - 512)\|I - 2 -- + -- 3 2 +-------+ 4 2 -- (64I + 384I - 1280I + 512)\|- I - 2 + 16I - 1152I + 256 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2691a:=integrate(1/(z^2+I*z-1)^(1/2)+(1-I*z)^(1/2), z= -1..1,"noPole") -- -- +---+ 2 -- 3I log((- 4I + 8)\|- I + I - 8I + 4) -- + -- +-+ 2 +-----+ -- - 3I log((- 4I - 8)\|I + I + 8I + 4) + (4I + 4)\|I + 1 -- + -- +-------+ -- (4I - 4)\|- I + 1 -- / -- 6I -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2720a:=integrate(acoth(1-(1-z)^(1/2))+atan(z-1), z= 0..1,"noPole") -- -- 5log(4) - %pi - 4 -- ----------------- -- 4 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2724a:=integrate(log(1-1/z^3)-(1+1/z^2)^(1/2), z= 0..%plusInfinity,"noPole") -- -- - infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2732:=integrate(atan(1/3*3^(1/2)*(2*z-1)), z= 0..%plusInfinity) -- -- - infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2783a:=integrate(1/z^(1/3)+atanh(1/z^(1/2)), z= 0..%plusInfinity,"noPole") -- -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2815a:=integrate((I*z)^(1/2)-(1+1/(I*z)^(1/2))^(1/2), z= -1..1,"noPole") -- -- +----------+ +--------+ -- | +---+ | +-+ -- |\|- I + 1 |\|I + 1 -- - 6log( |---------- + 1) + 6log( |-------- + 1) -- | +---+ | +-+ -- \| \|- I \| \|I -- + -- +--------+ -- | +-+ -- +-+ |\|I + 1 +-+ -- - 2\|I |-------- + 2\|I + 1 -- | +-+ -- \| \|I -- - 3log(------------------------------) -- +-+ -- \|I -- + -- +----------+ -- | +---+ -- +---+ |\|- I + 1 +---+ -- - 2\|- I |---------- + 2\|- I + 1 -- | +---+ -- \| \|- I -- 3log(------------------------------------) -- +---+ -- \|- I -- + -- +----------+ +--------+ -- | +---+ | +-+ -- +---+ |\|- I + 1 +-+ |\|I + 1 +-+ -- (12\|- I - 24I) |---------- + (- 12\|I - 24I) |-------- + 16I\|I -- | +---+ | +-+ -- \| \|- I \| \|I -- + -- +---+ -- 16I\|- I -- / -- 24I -- Type: Union(f1: OrderedCompletion Expression Integer,...) in285:=integrate(sqrt(1+sqrt(z-1)), z) -- -- +------------+ -- +-----+ | +-----+ -- (4\|z - 1 + 12z - 20)\|\|z - 1 + 1 -- ------------------------------------- -- 15 -- Type: Union(Expression Integer,...) in295a:=integrate(z*sqrt(1+sqrt(z^2-1)), z) -- -- +-------------+ -- +------+ | +------+ -- | 2 2 | | 2 -- (2\|z - 1 + 6z - 10)\|\|z - 1 + 1 -- --------------------------------------- -- 15 -- Type: Union(Expression Integer,...) in295ba:=integrate(z*sqrt(1+sqrt(z^2-1)), z= 1..sqrt(2),"noPole") -- -- +-+ -- 4\|2 + 4 -- --------- -- 15 -- Type: Union(f1: OrderedCompletion Expression Integer,...) integrate(1/sqrt(20+x^2+y^2), x = -5..5,"noPole") -- -- +-------+ +-------+ -- | 2 2 | 2 2 -- log(10\|y + 45 + y + 70) - log(- 10\|y + 45 + y + 70) -- ----------------------------------------------------------- -- 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) -- in291:=integrate(cos(2*atan(z-sqrt(2)))-sin(2*atan(z-sqrt(2))), z = 0..%plusInfinity) -- -- - infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2924a:=integrate(1/(I*z)^(1/2)+(1+1/(I*z)^(1/2))^(1/2), z= -1..1,"noPole") -- -- +----------+ +--------+ -- | +---+ | +-+ -- +---+ +-+ |\|- I + 1 +---+ +-+ |\|I + 1 -- 2\|- I \|I log( |---------- + 1) - 2\|- I \|I log( |-------- + 1) -- | +---+ | +-+ -- \| \|- I \| \|I -- + -- +--------+ -- | +-+ -- +-+ |\|I + 1 +-+ -- - 2\|I |-------- + 2\|I + 1 -- | +-+ -- +---+ +-+ \| \|I -- \|- I \|I log(------------------------------) -- +-+ -- \|I -- + -- +----------+ -- | +---+ -- +---+ |\|- I + 1 +---+ -- - 2\|- I |---------- + 2\|- I + 1 -- | +---+ -- +---+ +-+ \| \|- I -- - \|- I \|I log(------------------------------------) -- +---+ -- \|- I -- + -- +----------+ +--------+ -- | +---+ | +-+ -- +---+ +-+ |\|- I + 1 +---+ +-+ +---+ |\|I + 1 -- (8I\|- I + 4I)\|I |---------- + (8I\|- I \|I + 4I\|- I ) |-------- -- | +---+ | +-+ -- \| \|- I \| \|I -- + -- +-+ +---+ -- 16I\|I + 16I\|- I -- / -- +---+ +-+ -- 8I\|- I \|I -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2963a:=integrate(cosh(-1+(1-z)^(1/2))+(z^2+I*z-3)^(1/2), z= -1..1,"noPole") -- -- +-+ -- 4 2 \|2 - 1 +-------+ -- (- 16I - 128I + 768)%e %e \|- I - 2 -- + -- +-+ -- 5 4 3 2 \|2 - 1 -- (4I - 24I - 32I - 320I - 960I - 384)%e %e -- * -- +-----+ -- \|I - 2 -- + -- +-+ -- 5 4 3 2 \|2 - 1 +-------+ -- (4I + 24I - 32I + 320I - 960I + 384)%e %e \|- I - 2 -- + -- +-+ -- 6 4 2 \|2 - 1 -- (- I + 60I + 848I - 192)%e %e -- * -- +-------+ 2 -- log((- 4I + 8)\|- I - 2 + I - 8I - 4) -- + -- +-+ -- 4 2 \|2 - 1 +-------+ -- (16I + 128I - 768)%e %e \|- I - 2 -- + -- +-+ -- 5 4 3 2 \|2 - 1 -- (- 4I + 24I + 32I + 320I + 960I + 384)%e %e -- * -- +-----+ -- \|I - 2 -- + -- +-+ -- 5 4 3 2 \|2 - 1 +-------+ -- (- 4I - 24I + 32I - 320I + 960I - 384)%e %e \|- I - 2 -- + -- +-+ -- 6 4 2 \|2 - 1 -- (I - 60I - 848I + 192)%e %e -- * -- +-----+ 2 -- log((- 4I - 8)\|I - 2 + I + 8I - 4) -- + -- +-+ 2 -- 2 +-+ 2 \|2 - 1 -- ((256I - 1024)%e\|2 + (- 256I + 1024)%e)(%e ) -- + -- 2 2 3 2 -- ((256I - 1024)%e + (- 256I + 1024I)%e + 256I - 1024) -- * -- +-+ -- \|2 - 1 -- %e -- + -- 2 +-+ 2 -- (- 256I + 1024)%e\|2 + (- 256I + 1024)%e -- * -- +-------+ -- \|- I - 2 -- + -- 3 2 +-+ -- (- 64I + 384I + 1280I + 512)%e\|2 -- + -- 3 2 -- (64I - 384I - 1280I - 512)%e -- * -- +-+ 2 -- \|2 - 1 -- (%e ) -- + -- 3 2 2 -- (- 64I + 384I + 1280I + 512)%e -- + -- 5 4 3 2 3 2 -- (4I + 72I - 288I - 1088I + 64I + 1152)%e - 64I + 384I -- + -- 1280I + 512 -- * -- +-+ -- \|2 - 1 -- %e -- + -- 3 2 +-+ 3 2 -- (64I - 384I - 1280I - 512)%e\|2 + (64I - 384I - 1280I - 512)%e -- * -- +-----+ -- \|I - 2 -- + -- 3 2 +-+ -- (- 64I - 384I + 1280I - 512)%e\|2 -- + -- 3 2 -- (64I + 384I - 1280I + 512)%e -- * -- +-+ 2 -- \|2 - 1 -- (%e ) -- + -- 3 2 2 -- (- 64I - 384I + 1280I - 512)%e -- + -- 5 4 3 2 3 2 -- (- 4I + 72I + 288I - 1088I - 64I + 1152)%e - 64I - 384I -- + -- 1280I - 512 -- * -- +-+ -- \|2 - 1 -- %e -- + -- 3 2 +-+ 3 2 -- (64I + 384I - 1280I + 512)%e\|2 + (64I + 384I - 1280I + 512)%e -- * -- +-------+ -- \|- I - 2 -- + -- +-+ 2 -- 4 2 +-+ 4 2 \|2 - 1 -- ((16I - 1152I + 256)%e\|2 + (- 16I + 1152I - 256)%e)(%e ) -- + -- 4 2 2 5 3 4 2 -- (16I - 1152I + 256)%e + (- 32I + 768I - 2560I)%e + 16I - 1152I -- + -- 256 -- * -- +-+ -- \|2 - 1 -- %e -- + -- 4 2 +-+ 4 2 -- (- 16I + 1152I - 256)%e\|2 + (- 16I + 1152I - 256)%e -- / -- +-+ -- 2 \|2 - 1 +-------+ -- (256I - 1024)%e %e \|- I - 2 -- + -- +-+ -- 3 2 \|2 - 1 -- (- 64I + 384I + 1280I + 512)%e %e -- * -- +-----+ -- \|I - 2 -- + -- +-+ -- 3 2 \|2 - 1 +-------+ -- (- 64I - 384I + 1280I - 512)%e %e \|- I - 2 -- + -- +-+ -- 4 2 \|2 - 1 -- (16I - 1152I + 256)%e %e -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2992a:=integrate(acoth(1-z^(1/2))+log(1+z^(1/3)), z= 1..%plusInfinity,"noPole") -- -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in2997a:=integrate(log(1+1/z^3)-log(abs(1+z)), z= %minusInfinity..%plusInfinity,"noPole") -- -- - infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in3001a:=integrate(((I*z)^(1/2)-1)/(-2+(I*z)^(1/2)), z= 0..%plusInfinity,"noPole") -- -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in3008a:=integrate(exp(-z^(1/3))+atanh(1/z^(1/2)), z= 0..%plusInfinity,"noPole") -- -- + infinity -- Type: Union(f1: OrderedCompletion Expression Integer,...) in303a:=integrate(1/(1+cosh(n*z)^2), z= 0..1,"noPole") -- -- log -- +-+ - n 8 +-+ - n 6 -- (- 816\|2 + 1154)(%e ) + (- 560\|2 + 792)(%e ) -- + -- +-+ - n 4 +-+ - n 2 -- (- 144\|2 + 204)(%e ) + (- 16\|2 + 24)(%e ) + 2 -- / -- - n 8 - n 6 - n 4 - n 2 -- (%e ) + 12(%e ) + 38(%e ) + 12(%e ) + 1 -- + -- +-+ -- - log(- 24\|2 + 34) -- / -- +-+ -- 4n\|2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in314a:=integrate(1/(sin(z)-1/2), z= 0..1,"noPole") -- -- log -- 2 2 -- - 12sin(1) + (42cos(1) + 48)sin(1) - 36cos(1) - 84cos(1) -- + -- - 48 -- * -- +-+ -- \|3 -- + -- 2 2 -- 21sin(1) + (- 72cos(1) - 84)sin(1) + 63cos(1) + 144cos(1) + 84 -- / -- 2 -- 4sin(1) - 4sin(1) + 1 -- + -- +-+ -- - log(- 168\|3 + 291) -- / -- +-+ -- \|3 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in317:=integrate((cos(z)^a)^(1/a), z= 0..%pi) -- -- 0 -- Type: Union(f1: OrderedCompletion Expression Integer,...) in319a:=integrate(exp(-z)*atan(sin(z)/(1+cos(z))), z=0..%plusInfinity,"noPole") -- -- 1 -- - -- 2 -- Type: Union(f1: OrderedCompletion Expression Integer,...) @ \eject \begin{thebibliography}{99} \bibitem{1} nothing \end{thebibliography} \end{document}