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|
\begin{patch}{ExIntRationalWithRealParameterPatch1}
\begin{paste}{ExIntRationalWithRealParameterFull1}{ExIntRationalWithRealParameterEmpty1}
\pastebutton{ExIntRationalWithRealParameterFull1}{\hidepaste}
\tab{5}\spadcommand{integrate(1/(x**2 + a),x)}
\indentrel{3}\begin{verbatim}
2 ���Ŀ
(x - a)\�- a + 2a x �Ŀ
log(���������������������) x\�a
2 atan(�����)
x + a a
(1) [��������������������������,�����������]
���Ŀ �Ŀ
2\�- a \�a
Type: Union(List Expression Integer,...)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExIntRationalWithRealParameterEmpty1}
\begin{paste}{ExIntRationalWithRealParameterEmpty1}{ExIntRationalWithRealParameterPatch1}
\pastebutton{ExIntRationalWithRealParameterEmpty1}{\showpaste}
\tab{5}\spadcommand{integrate(1/(x**2 + a),x)}
\end{paste}\end{patch}
\begin{patch}{ExIntRationalFunctionPatch1}
\begin{paste}{ExIntRationalFunctionFull1}{ExIntRationalFunctionEmpty1}
\pastebutton{ExIntRationalFunctionFull1}{\hidepaste}
\tab{5}\spadcommand{integrate((x**2+2*x+1)/((x+1)**6+1),x)}
\indentrel{3}\begin{verbatim}
3 2
atan(x + 3x + 3x + 1)
(1) �����������������������
3
Type: Union(Expression Integer,...)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExIntRationalFunctionEmpty1}
\begin{paste}{ExIntRationalFunctionEmpty1}{ExIntRationalFunctionPatch1}
\pastebutton{ExIntRationalFunctionEmpty1}{\showpaste}
\tab{5}\spadcommand{integrate((x**2+2*x+1)/((x+1)**6+1),x)}
\end{paste}\end{patch}
\begin{patch}{ExIntRationalFunctionPatch2}
\begin{paste}{ExIntRationalFunctionFull2}{ExIntRationalFunctionEmpty2}
\pastebutton{ExIntRationalFunctionFull2}{\hidepaste}
\tab{5}\spadcommand{integrate(1/(x**3+x+1),x)\bound{i }}
\indentrel{3}\begin{verbatim}
(2)
��������������Ŀ
� 2
�- 93%%H0 + 12
( ��������������� - %%H0)
\� 31
*
log
��������������Ŀ
� 2
�- 93%%H0 + 12 2
(62%%H0 + 31) ��������������� + 62%%H0
\� 31
+
- 31%%H0 + 18x - 4
+
��������������Ŀ
� 2
�- 93%%H0 + 12
(- ��������������� - %%H0)
\� 31
*
log
��������������Ŀ
� 2
�- 93%%H0 + 12 2
(- 62%%H0 - 31) ��������������� + 62%%H0
\� 31
+
- 31%%H0 + 18x - 4
+
2
2%%H0 log(- 62%%H0 + 31%%H0 + 9x + 4)
/
2
Type: Union(Expression Integer,...)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExIntRationalFunctionEmpty2}
\begin{paste}{ExIntRationalFunctionEmpty2}{ExIntRationalFunctionPatch2}
\pastebutton{ExIntRationalFunctionEmpty2}{\showpaste}
\tab{5}\spadcommand{integrate(1/(x**3+x+1),x)\bound{i }}
\end{paste}\end{patch}
\begin{patch}{ExIntRationalFunctionPatch3}
\begin{paste}{ExIntRationalFunctionFull3}{ExIntRationalFunctionEmpty3}
\pastebutton{ExIntRationalFunctionFull3}{\hidepaste}
\tab{5}\spadcommand{definingPolynomial(tower(\%).2::EXPR INT)\free{i }}
\indentrel{3}\begin{verbatim}
3
31%%H0 - 3%%H0 - 1
(3) �������������������
31
Type: Expression Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExIntRationalFunctionEmpty3}
\begin{paste}{ExIntRationalFunctionEmpty3}{ExIntRationalFunctionPatch3}
\pastebutton{ExIntRationalFunctionEmpty3}{\showpaste}
\tab{5}\spadcommand{definingPolynomial(tower(\%).2::EXPR INT)\free{i }}
\end{paste}\end{patch}
\begin{patch}{ExIntAlgebraicRelationPatch1}
\begin{paste}{ExIntAlgebraicRelationFull1}{ExIntAlgebraicRelationEmpty1}
\pastebutton{ExIntAlgebraicRelationFull1}{\hidepaste}
\tab{5}\spadcommand{integrate(tan(atan(x)/3),x)}
\indentrel{3}\begin{verbatim}
(1)
atan(x) 2 atan(x) 2
8log(3tan(�������) - 1) - 3tan(�������)
3 3
+
atan(x)
18x tan(�������)
3
/
18
Type: Union(Expression Integer,...)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExIntAlgebraicRelationEmpty1}
\begin{paste}{ExIntAlgebraicRelationEmpty1}{ExIntAlgebraicRelationPatch1}
\pastebutton{ExIntAlgebraicRelationEmpty1}{\showpaste}
\tab{5}\spadcommand{integrate(tan(atan(x)/3),x)}
\end{paste}\end{patch}
\begin{patch}{ExIntRationalWithComplexParameterPatch1}
\begin{paste}{ExIntRationalWithComplexParameterFull1}{ExIntRationalWithComplexParameterEmpty1}
\pastebutton{ExIntRationalWithComplexParameterFull1}{\hidepaste}
\tab{5}\spadcommand{complexIntegrate(1/(x**2 + a),x)}
\indentrel{3}\begin{verbatim}
���Ŀ ���Ŀ
x\�- a + a x\�- a - a
log(�����������) - log(�����������)
���Ŀ ���Ŀ
\�- a \�- a
(1) �����������������������������������
���Ŀ
2\�- a
Type: Expression Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExIntRationalWithComplexParameterEmpty1}
\begin{paste}{ExIntRationalWithComplexParameterEmpty1}{ExIntRationalWithComplexParameterPatch1}
\pastebutton{ExIntRationalWithComplexParameterEmpty1}{\showpaste}
\tab{5}\spadcommand{complexIntegrate(1/(x**2 + a),x)}
\end{paste}\end{patch}
\begin{patch}{ExIntNoSolutionPatch1}
\begin{paste}{ExIntNoSolutionFull1}{ExIntNoSolutionEmpty1}
\pastebutton{ExIntNoSolutionFull1}{\hidepaste}
\tab{5}\spadcommand{integrate(log(1 + sqrt(a*x + b)) / x,x)}
\indentrel{3}\begin{verbatim}
x ��������Ŀ
ڿ log(\�b + %T a + 1)
(1) � �������������������� d%T
�� %T
Type: Union(Expression Integer,...)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExIntNoSolutionEmpty1}
\begin{paste}{ExIntNoSolutionEmpty1}{ExIntNoSolutionPatch1}
\pastebutton{ExIntNoSolutionEmpty1}{\showpaste}
\tab{5}\spadcommand{integrate(log(1 + sqrt(a*x + b)) / x,x)}
\end{paste}\end{patch}
\begin{patch}{ExIntTwoSimilarIntegrandsPatch1}
\begin{paste}{ExIntTwoSimilarIntegrandsFull1}{ExIntTwoSimilarIntegrandsEmpty1}
\pastebutton{ExIntTwoSimilarIntegrandsFull1}{\hidepaste}
\tab{5}\spadcommand{integrate(x**3 / (a+b*x)**(1/3),x)}
\indentrel{3}\begin{verbatim}
(1)
3 3 2 2 2 3 3�������Ŀ2
(120b x - 135a b x + 162a b x - 243a )\�b x + a
���������������������������������������������������
4
440b
Type: Union(Expression Integer,...)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExIntTwoSimilarIntegrandsEmpty1}
\begin{paste}{ExIntTwoSimilarIntegrandsEmpty1}{ExIntTwoSimilarIntegrandsPatch1}
\pastebutton{ExIntTwoSimilarIntegrandsEmpty1}{\showpaste}
\tab{5}\spadcommand{integrate(x**3 / (a+b*x)**(1/3),x)}
\end{paste}\end{patch}
\begin{patch}{ExIntTwoSimilarIntegrandsPatch2}
\begin{paste}{ExIntTwoSimilarIntegrandsFull2}{ExIntTwoSimilarIntegrandsEmpty2}
\pastebutton{ExIntTwoSimilarIntegrandsFull2}{\hidepaste}
\tab{5}\spadcommand{integrate(1 / (x**3 * (a+b*x)**(1/3)),x)}
\indentrel{3}\begin{verbatim}
(2)
-
2 2 �Ŀ
2b x \�3
*
3�Ŀ3�������Ŀ2 3�Ŀ2 3�������Ŀ
log(\�a \�b x + a + \�a \�b x + a + a)
+
2 2 �Ŀ 3�Ŀ2 3�������Ŀ
4b x \�3 log(\�a \�b x + a - a)
+
�Ŀ3�Ŀ2 3�������Ŀ �Ŀ
2 2 2\�3 \�a \�b x + a + a\�3
12b x atan(����������������������������)
3a
+
�Ŀ3�Ŀ3�������Ŀ2
(12b x - 9a)\�3 \�a \�b x + a
/
2 2 �Ŀ3�Ŀ
18a x \�3 \�a
Type: Union(Expression Integer,...)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExIntTwoSimilarIntegrandsEmpty2}
\begin{paste}{ExIntTwoSimilarIntegrandsEmpty2}{ExIntTwoSimilarIntegrandsPatch2}
\pastebutton{ExIntTwoSimilarIntegrandsEmpty2}{\showpaste}
\tab{5}\spadcommand{integrate(1 / (x**3 * (a+b*x)**(1/3)),x)}
\end{paste}\end{patch}
\begin{patch}{ExIntRadicalOfTranscendentalPatch1}
\begin{paste}{ExIntRadicalOfTranscendentalFull1}{ExIntRadicalOfTranscendentalEmpty1}
\pastebutton{ExIntRadicalOfTranscendentalFull1}{\hidepaste}
\tab{5}\spadcommand{integrate((x + 1) / (x * (x + log x)**(3/2)),x)}
\indentrel{3}\begin{verbatim}
����������Ŀ
2\�log(x) + x
(1) - ��������������
log(x) + x
Type: Union(Expression Integer,...)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExIntRadicalOfTranscendentalEmpty1}
\begin{paste}{ExIntRadicalOfTranscendentalEmpty1}{ExIntRadicalOfTranscendentalPatch1}
\pastebutton{ExIntRadicalOfTranscendentalEmpty1}{\showpaste}
\tab{5}\spadcommand{integrate((x + 1) / (x * (x + log x)**(3/2)),x)}
\end{paste}\end{patch}
\begin{patch}{ExIntNonElementaryPatch1}
\begin{paste}{ExIntNonElementaryFull1}{ExIntNonElementaryEmpty1}
\pastebutton{ExIntNonElementaryFull1}{\hidepaste}
\tab{5}\spadcommand{integrate(exp(-x**2) * erf(x) / (erf(x)**3 - erf(x)**2 - erf(x) + 1),x)}
\indentrel{3}\begin{verbatim}
���Ŀ erf(x) - 1 ���Ŀ
(erf(x) - 1)\�%pi log(����������) - 2\�%pi
erf(x) + 1
(1) �������������������������������������������
8erf(x) - 8
Type: Union(Expression Integer,...)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExIntNonElementaryEmpty1}
\begin{paste}{ExIntNonElementaryEmpty1}{ExIntNonElementaryPatch1}
\pastebutton{ExIntNonElementaryEmpty1}{\showpaste}
\tab{5}\spadcommand{integrate(exp(-x**2) * erf(x) / (erf(x)**3 - erf(x)**2 - erf(x) + 1),x)}
\end{paste}\end{patch}
\begin{patch}{ExIntTrigPatch1}
\begin{paste}{ExIntTrigFull1}{ExIntTrigEmpty1}
\pastebutton{ExIntTrigFull1}{\hidepaste}
\tab{5}\spadcommand{integrate((sinh(1+sqrt(x+b))+2*sqrt(x+b))/(sqrt(x+b)*(x+cosh(1+sqrt(x+b)))),x)}
\indentrel{3}\begin{verbatim}
(1)
�����Ŀ
- 2cosh(\�x + b + 1) - 2x
2log(���������������������������������������)
�����Ŀ �����Ŀ
sinh(\�x + b + 1) - cosh(\�x + b + 1)
+
�����Ŀ
- 2\�x + b
Type: Union(Expression Integer,...)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExIntTrigEmpty1}
\begin{paste}{ExIntTrigEmpty1}{ExIntTrigPatch1}
\pastebutton{ExIntTrigEmpty1}{\showpaste}
\tab{5}\spadcommand{integrate((sinh(1+sqrt(x+b))+2*sqrt(x+b))/(sqrt(x+b)*(x+cosh(1+sqrt(x+b)))),x)}
\end{paste}\end{patch}
|
