Integrals 401 to 500

Sympy [F(-2)]

Exception generated. \[ \int F^{c (a+b x)} (d+e x)^{-m} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(F**((b*x+a)*c)/((e*x+d)**m),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/2_Exponentials/156_2.1

Test file number \(156\)

Integral number in file \(85\)

Sympy [F(-2)]

Exception generated. \[ \int e^{n \text {arctanh}(a x)} (c-a c x)^{5/2} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(exp(n*atanh(a*x))*(-a*c*x+c)**(5/2),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/163_2.5.3

Test file number \(163\)

Integral number in file \(286\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{-\text {arctanh}(a x)}}{c-\frac {c}{a x}} \, dx=\text {Exception raised: TypeError} \] Input:

integrate(1/(a*x+1)*(-a**2*x**2+1)**(1/2)/(c-c/a/x),x)
 

Output:

Exception raised: TypeError >> Invalid comparison of non-real zoo
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/163_2.5.3

Test file number \(163\)

Integral number in file \(522\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{n \text {arctanh}(a x)}}{\left (c-\frac {c}{a^2 x^2}\right )^{5/2}} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(exp(n*atanh(a*x))/(c-c/a**2/x**2)**(5/2),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/163_2.5.3

Test file number \(163\)

Integral number in file \(785\)

Sympy [F(-2)]

Exception generated. \[ \int e^{n \coth ^{-1}(a x)} (c-a c x)^{5/2} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(exp(n*acoth(a*x))*(-a*c*x+c)**(5/2),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/164_2.5.4

Test file number \(164\)

Integral number in file \(291\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{n \coth ^{-1}(a x)}}{(c-a c x)^{7/2}} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(exp(n*acoth(a*x))/(-a*c*x+c)**(7/2),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/164_2.5.4

Test file number \(164\)

Integral number in file \(297\)

Sympy [F(-2)]

Exception generated. \[ \int e^{n \text {arctanh}(a x)} (c-a c x)^{5/2} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(exp(n*atanh(a*x))*(-a*c*x+c)**(5/2),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/167_x2.5.3

Test file number \(167\)

Integral number in file \(271\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{-\text {arctanh}(a x)}}{c-\frac {c}{a x}} \, dx=\text {Exception raised: TypeError} \] Input:

integrate(1/(a*x+1)*(-a**2*x**2+1)**(1/2)/(c-c/a/x),x)
 

Output:

Exception raised: TypeError >> Invalid comparison of non-real zoo
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/167_x2.5.3

Test file number \(167\)

Integral number in file \(507\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {e^{n \text {arctanh}(a x)}}{\left (c-\frac {c}{a^2 x^2}\right )^{5/2}} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(exp(n*atanh(a*x))/(c-c/a**2/x**2)**(5/2),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/167_x2.5.3

Test file number \(167\)

Integral number in file \(770\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\log \left (\frac {2 x \left (d \sqrt {-\frac {e}{d}}+e x\right )}{d+e x^2}\right )}{d+e x^2} \, dx=\text {Exception raised: TypeError} \] Input:

integrate(ln(2*x*(d*(-e/d)**(1/2)+e*x)/(e*x**2+d))/(e*x**2+d),x)
 

Output:

Exception raised: TypeError >> Invalid comparison of non-real zoo
 

input file name test_cases/rubi_tests/3_Logarithms/168_3_Logarithm_functions

Test file number \(168\)

Integral number in file \(40\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\log \left (-\frac {2 x \left (d \sqrt {-\frac {e}{d}}-e x\right )}{d+e x^2}\right )}{d+e x^2} \, dx=\text {Exception raised: TypeError} \] Input:

integrate(ln(-2*x*(d*(-e/d)**(1/2)-e*x)/(e*x**2+d))/(e*x**2+d),x)
 

Output:

Exception raised: TypeError >> Invalid comparison of non-real zoo
 

input file name test_cases/rubi_tests/3_Logarithms/168_3_Logarithm_functions

Test file number \(168\)

Integral number in file \(41\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\log \left (\frac {2 x \left (\frac {d \sqrt {e}}{\sqrt {-d}}+e x\right )}{d+e x^2}\right )}{d+e x^2} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(ln(2*x*(d*e**(1/2)/(-d)**(1/2)+e*x)/(e*x**2+d))/(e*x**2+d),x)
 

Output:

Exception raised: AttributeError >> 'NoneType' object has no attribute 'pr 
imitive'
 

input file name test_cases/rubi_tests/3_Logarithms/168_3_Logarithm_functions

Test file number \(168\)

Integral number in file \(42\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\log \left (-\frac {2 x \left (\frac {d \sqrt {e}}{\sqrt {-d}}-e x\right )}{d+e x^2}\right )}{d+e x^2} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(ln(-2*x*(d*e**(1/2)/(-d)**(1/2)-e*x)/(e*x**2+d))/(e*x**2+d),x)
 

Output:

Exception raised: AttributeError >> 'NoneType' object has no attribute 'pr 
imitive'
 

input file name test_cases/rubi_tests/3_Logarithms/168_3_Logarithm_functions

Test file number \(168\)

Integral number in file \(43\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\log \left (\frac {2 x \left (\sqrt {d} \sqrt {-e}+e x\right )}{d+e x^2}\right )}{d+e x^2} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(ln(2*x*(d**(1/2)*(-e)**(1/2)+e*x)/(e*x**2+d))/(e*x**2+d),x)
 

Output:

Exception raised: AttributeError >> 'NoneType' object has no attribute 'pr 
imitive'
 

input file name test_cases/rubi_tests/3_Logarithms/168_3_Logarithm_functions

Test file number \(168\)

Integral number in file \(44\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\log \left (-\frac {2 x \left (\sqrt {d} \sqrt {-e}-e x\right )}{d+e x^2}\right )}{d+e x^2} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(ln(-2*x*(d**(1/2)*(-e)**(1/2)-e*x)/(e*x**2+d))/(e*x**2+d),x)
 

Output:

Exception raised: AttributeError >> 'NoneType' object has no attribute 'pr 
imitive'
                                                                                    
                                                                                    
 

input file name test_cases/rubi_tests/3_Logarithms/168_3_Logarithm_functions

Test file number \(168\)

Integral number in file \(45\)

Sympy [F(-2)]

Exception generated. \[ \int \log ^2\left (1+x+x^2\right ) \, dx=\text {Exception raised: RecursionError} \] Input:

integrate(ln(x**2+x+1)**2,x)
 

Output:

Exception raised: RecursionError >> maximum recursion depth exceeded in co 
mparison
 

input file name test_cases/rubi_tests/3_Logarithms/168_3_Logarithm_functions

Test file number \(168\)

Integral number in file \(99\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\log ^2\left (-1+x+x^2\right )}{x^3} \, dx=\text {Exception raised: RecursionError} \] Input:

integrate(ln(x**2+x-1)**2/x**3,x)
 

Output:

Exception raised: RecursionError >> maximum recursion depth exceeded while 
 calling a Python object
 

input file name test_cases/rubi_tests/3_Logarithms/168_3_Logarithm_functions

Test file number \(168\)

Integral number in file \(100\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (a+b \log \left (c \sqrt {x}\right )\right )^p}{x^4} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((a+b*ln(c*x**(1/2)))**p/x**4,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/169_3.1

Test file number \(169\)

Integral number in file \(190\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {x^{-1+n} \log \left (e x^n\right )}{1-e x^n} \, dx=\text {Exception raised: TypeError} \] Input:

integrate(x**(-1+n)*ln(e*x**n)/(1-e*x**n),x)
 

Output:

Exception raised: TypeError >> Invalid comparison of non-real zoo
 

input file name test_cases/rubi_tests/3_Logarithms/170_3.2

Test file number \(170\)

Integral number in file \(343\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {x^{-1+n} \log \left (\frac {x^n}{d}\right )}{d-x^n} \, dx=\text {Exception raised: TypeError} \] Input:

integrate(x**(-1+n)*ln(x**n/d)/(d-x**n),x)
 

Output:

Exception raised: TypeError >> Invalid comparison of non-real zoo
 

input file name test_cases/rubi_tests/3_Logarithms/170_3.2

Test file number \(170\)

Integral number in file \(344\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {x^{-1+n} \log \left (-\frac {e x^n}{d}\right )}{d+e x^n} \, dx=\text {Exception raised: TypeError} \] Input:

integrate(x**(-1+n)*ln(-e*x**n/d)/(d+e*x**n),x)
                                                                                    
                                                                                    
 

Output:

Exception raised: TypeError >> Invalid comparison of non-real zoo
 

input file name test_cases/rubi_tests/3_Logarithms/170_3.2

Test file number \(170\)

Integral number in file \(345\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {a+b \log \left (c x^n\right )}{x \left (c-x^{-n}\right )} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((a+b*ln(c*x**n))/x/(c-x**(-n)),x)
 

Output:

Exception raised: TypeError >> Invalid comparison of non-real zoo
 

input file name test_cases/rubi_tests/3_Logarithms/170_3.2

Test file number \(170\)

Integral number in file \(418\)

Sympy [F(-2)]

Exception generated. \[ \int (f x)^m \left (d+e x^r\right )^3 \left (a+b \log \left (c x^n\right )\right ) \, dx=\text {Exception raised: TypeError} \] Input:

integrate((f*x)**m*(d+e*x**r)**3*(a+b*ln(c*x**n)),x)
 

Output:

Exception raised: TypeError >> Invalid comparison of non-real zoo
 

input file name test_cases/rubi_tests/3_Logarithms/170_3.2

Test file number \(170\)

Integral number in file \(438\)

Sympy [F(-2)]

Exception generated. \[ \int (f x)^m \left (d+e x^r\right )^2 \left (a+b \log \left (c x^n\right )\right ) \, dx=\text {Exception raised: TypeError} \] Input:

integrate((f*x)**m*(d+e*x**r)**2*(a+b*ln(c*x**n)),x)
 

Output:

Exception raised: TypeError >> Invalid comparison of non-real zoo
 

input file name test_cases/rubi_tests/3_Logarithms/170_3.2

Test file number \(170\)

Integral number in file \(439\)

Sympy [F(-2)]

Exception generated. \[ \int (f x)^m \left (d+e x^r\right ) \left (a+b \log \left (c x^n\right )\right ) \, dx=\text {Exception raised: TypeError} \] Input:

integrate((f*x)**m*(d+e*x**r)*(a+b*ln(c*x**n)),x)
 

Output:

Exception raised: TypeError >> Invalid comparison of non-real zoo
 

input file name test_cases/rubi_tests/3_Logarithms/170_3.2

Test file number \(170\)

Integral number in file \(440\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (a+b \log \left (c x^n\right )\right )^4 \log \left (d \left (\frac {1}{d}+f x^m\right )\right )}{x} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((a+b*ln(c*x**n))**4*ln(d*(1/d+f*x**m))/x,x)
 

Output:

Exception raised: TypeError >> Invalid comparison of non-real zoo
 

input file name test_cases/rubi_tests/3_Logarithms/171_3.3

Test file number \(171\)

Integral number in file \(70\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (a+b \log \left (c x^n\right )\right )^3 \log \left (d \left (\frac {1}{d}+f x^m\right )\right )}{x} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((a+b*ln(c*x**n))**3*ln(d*(1/d+f*x**m))/x,x)
 

Output:

Exception raised: TypeError >> Invalid comparison of non-real zoo
 

input file name test_cases/rubi_tests/3_Logarithms/171_3.3

Test file number \(171\)

Integral number in file \(71\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (a+b \log \left (c x^n\right )\right )^2 \log \left (d \left (\frac {1}{d}+f x^m\right )\right )}{x} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((a+b*ln(c*x**n))**2*ln(d*(1/d+f*x**m))/x,x)
 

Output:

Exception raised: TypeError >> Invalid comparison of non-real zoo
 

input file name test_cases/rubi_tests/3_Logarithms/171_3.3

Test file number \(171\)

Integral number in file \(72\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (a+b \log \left (c x^n\right )\right ) \log \left (d \left (\frac {1}{d}+f x^m\right )\right )}{x} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((a+b*ln(c*x**n))*ln(d*(1/d+f*x**m))/x,x)
 

Output:

Exception raised: TypeError >> Invalid comparison of non-real zoo
 

input file name test_cases/rubi_tests/3_Logarithms/171_3.3

Test file number \(171\)

Integral number in file \(73\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (a+b \log \left (c x^n\right )\right )^3 \log \left (d \left (e+f x^m\right )^r\right )}{x} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((a+b*ln(c*x**n))**3*ln(d*(e+f*x**m)**r)/x,x)
 

Output:

Exception raised: TypeError >> Invalid comparison of non-real zoo
 

input file name test_cases/rubi_tests/3_Logarithms/171_3.3

Test file number \(171\)

Integral number in file \(145\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (a+b \log \left (c x^n\right )\right )^2 \log \left (d \left (e+f x^m\right )^r\right )}{x} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((a+b*ln(c*x**n))**2*ln(d*(e+f*x**m)**r)/x,x)
 

Output:

Exception raised: TypeError >> Invalid comparison of non-real zoo
 

input file name test_cases/rubi_tests/3_Logarithms/171_3.3

Test file number \(171\)

Integral number in file \(146\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (a+b \log \left (c x^n\right )\right ) \log \left (d \left (e+f x^m\right )^r\right )}{x} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((a+b*ln(c*x**n))*ln(d*(e+f*x**m)**r)/x,x)
 

Output:

Exception raised: TypeError >> Invalid comparison of non-real zoo
 

input file name test_cases/rubi_tests/3_Logarithms/171_3.3

Test file number \(171\)

Integral number in file \(147\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (a+b \log \left (c x^n\right )\right ) \log \left (d \left (e+f x^m\right )^k\right )}{x} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((a+b*ln(c*x**n))*ln(d*(e+f*x**m)**k)/x,x)
 

Output:

Exception raised: TypeError >> Invalid comparison of non-real zoo
 

input file name test_cases/rubi_tests/3_Logarithms/171_3.3

Test file number \(171\)

Integral number in file \(153\)

Sympy [F(-2)]

Exception generated. \[ \int (a+b x)^4 \left (A+B \log \left (e (a+b x)^n (c+d x)^{-n}\right )\right ) \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)**4*(A+B*ln(e*(b*x+a)**n/((d*x+c)**n))),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/172_3.4

Test file number \(172\)

Integral number in file \(147\)

Sympy [F(-2)]

Exception generated. \[ \int (a+b x)^3 \left (A+B \log \left (e (a+b x)^n (c+d x)^{-n}\right )\right ) \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)**3*(A+B*ln(e*(b*x+a)**n/((d*x+c)**n))),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/172_3.4

Test file number \(172\)

Integral number in file \(148\)

Sympy [F(-2)]

Exception generated. \[ \int (a+b x)^2 \left (A+B \log \left (e (a+b x)^n (c+d x)^{-n}\right )\right ) \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)**2*(A+B*ln(e*(b*x+a)**n/((d*x+c)**n))),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
                                                                                    
                                                                                    
 

input file name test_cases/rubi_tests/3_Logarithms/172_3.4

Test file number \(172\)

Integral number in file \(149\)

Sympy [F(-2)]

Exception generated. \[ \int (a+b x) \left (A+B \log \left (e (a+b x)^n (c+d x)^{-n}\right )\right ) \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)*(A+B*ln(e*(b*x+a)**n/((d*x+c)**n))),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/172_3.4

Test file number \(172\)

Integral number in file \(150\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {A+B \log \left (e (a+b x)^n (c+d x)^{-n}\right )}{(a+b x)^2} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((A+B*ln(e*(b*x+a)**n/((d*x+c)**n)))/(b*x+a)**2,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/172_3.4

Test file number \(172\)

Integral number in file \(152\)

Sympy [F(-2)]

Exception generated. \[ \int (a+b x)^3 \left (A+B \log \left (e (a+b x)^n (c+d x)^{-n}\right )\right )^2 \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)**3*(A+B*ln(e*(b*x+a)**n/((d*x+c)**n)))**2,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/172_3.4

Test file number \(172\)

Integral number in file \(156\)

Sympy [F(-2)]

Exception generated. \[ \int (a+b x)^2 \left (A+B \log \left (e (a+b x)^n (c+d x)^{-n}\right )\right )^2 \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)**2*(A+B*ln(e*(b*x+a)**n/((d*x+c)**n)))**2,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/172_3.4

Test file number \(172\)

Integral number in file \(157\)

Sympy [F(-2)]

Exception generated. \[ \int (a+b x) \left (A+B \log \left (e (a+b x)^n (c+d x)^{-n}\right )\right )^2 \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)*(A+B*ln(e*(b*x+a)**n/((d*x+c)**n)))**2,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/172_3.4

Test file number \(172\)

Integral number in file \(158\)

Sympy [F(-2)]

Exception generated. \[ \int (a+b x)^3 \left (A+B \log \left (e (a+b x)^n (c+d x)^{-n}\right )\right )^3 \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)**3*(A+B*ln(e*(b*x+a)**n/((d*x+c)**n)))**3,x)
                                                                                    
                                                                                    
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/172_3.4

Test file number \(172\)

Integral number in file \(164\)

Sympy [F(-2)]

Exception generated. \[ \int (a+b x)^2 \left (A+B \log \left (e (a+b x)^n (c+d x)^{-n}\right )\right )^3 \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)**2*(A+B*ln(e*(b*x+a)**n/((d*x+c)**n)))**3,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/172_3.4

Test file number \(172\)

Integral number in file \(165\)

Sympy [F(-2)]

Exception generated. \[ \int (a+b x) \left (A+B \log \left (e (a+b x)^n (c+d x)^{-n}\right )\right )^3 \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)*(A+B*ln(e*(b*x+a)**n/((d*x+c)**n)))**3,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/172_3.4

Test file number \(172\)

Integral number in file \(166\)

Sympy [F(-2)]

Exception generated. \[ \int (g+h x)^4 \left (A+B \log \left (e (a+b x)^n (c+d x)^{-n}\right )\right ) \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((h*x+g)**4*(A+B*ln(e*(b*x+a)**n/((d*x+c)**n))),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/172_3.4

Test file number \(172\)

Integral number in file \(293\)

Sympy [F(-2)]

Exception generated. \[ \int (g+h x)^3 \left (A+B \log \left (e (a+b x)^n (c+d x)^{-n}\right )\right ) \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((h*x+g)**3*(A+B*ln(e*(b*x+a)**n/((d*x+c)**n))),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/172_3.4

Test file number \(172\)

Integral number in file \(294\)

Sympy [F(-2)]

Exception generated. \[ \int (g+h x)^2 \left (A+B \log \left (e (a+b x)^n (c+d x)^{-n}\right )\right ) \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((h*x+g)**2*(A+B*ln(e*(b*x+a)**n/((d*x+c)**n))),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/172_3.4

Test file number \(172\)

Integral number in file \(295\)

Sympy [F(-2)]

Exception generated. \[ \int (g+h x) \left (A+B \log \left (e (a+b x)^n (c+d x)^{-n}\right )\right ) \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((h*x+g)*(A+B*ln(e*(b*x+a)**n/((d*x+c)**n))),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/172_3.4

Test file number \(172\)

Integral number in file \(296\)

Sympy [F(-2)]

Exception generated. \[ \int \left (A+B \log \left (e (a+b x)^n (c+d x)^{-n}\right )\right ) \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(A+B*ln(e*(b*x+a)**n/((d*x+c)**n)),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/172_3.4

Test file number \(172\)

Integral number in file \(297\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {A+B \log \left (e (a+b x)^n (c+d x)^{-n}\right )}{g+h x} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((A+B*ln(e*(b*x+a)**n/((d*x+c)**n)))/(h*x+g),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/172_3.4

Test file number \(172\)

Integral number in file \(298\)

Sympy [F(-2)]

Exception generated. \[ \int (g+h x)^2 \left (A+B \log \left (e (a+b x)^n (c+d x)^{-n}\right )\right )^2 \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((h*x+g)**2*(A+B*ln(e*(b*x+a)**n/((d*x+c)**n)))**2,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/172_3.4

Test file number \(172\)

Integral number in file \(303\)

Sympy [F(-2)]

Exception generated. \[ \int (g+h x) \left (A+B \log \left (e (a+b x)^n (c+d x)^{-n}\right )\right )^2 \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((h*x+g)*(A+B*ln(e*(b*x+a)**n/((d*x+c)**n)))**2,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/172_3.4

Test file number \(172\)

Integral number in file \(304\)

Sympy [F(-2)]

Exception generated. \[ \int \left (A+B \log \left (e (a+b x)^n (c+d x)^{-n}\right )\right )^2 \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((A+B*ln(e*(b*x+a)**n/((d*x+c)**n)))**2,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/172_3.4

Test file number \(172\)

Integral number in file \(305\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (A+B \log \left (e (a+b x)^n (c+d x)^{-n}\right )\right )^2}{g+h x} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((A+B*ln(e*(b*x+a)**n/((d*x+c)**n)))**2/(h*x+g),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/172_3.4

Test file number \(172\)

Integral number in file \(306\)

Sympy [F(-2)]

Exception generated. \[ \int (g+h x)^2 \left (A+B \log \left (e (a+b x)^n (c+d x)^{-n}\right )\right )^3 \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((h*x+g)**2*(A+B*ln(e*(b*x+a)**n/((d*x+c)**n)))**3,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/172_3.4

Test file number \(172\)

Integral number in file \(309\)

Sympy [F(-2)]

Exception generated. \[ \int (g+h x) \left (A+B \log \left (e (a+b x)^n (c+d x)^{-n}\right )\right )^3 \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((h*x+g)*(A+B*ln(e*(b*x+a)**n/((d*x+c)**n)))**3,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/172_3.4

Test file number \(172\)

Integral number in file \(310\)

Sympy [F(-2)]

Exception generated. \[ \int \left (A+B \log \left (e (a+b x)^n (c+d x)^{-n}\right )\right )^3 \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((A+B*ln(e*(b*x+a)**n/((d*x+c)**n)))**3,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
                                                                                    
                                                                                    
 

input file name test_cases/rubi_tests/3_Logarithms/172_3.4

Test file number \(172\)

Integral number in file \(311\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (A+B \log \left (e (a+b x)^n (c+d x)^{-n}\right )\right )^3}{g+h x} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((A+B*ln(e*(b*x+a)**n/((d*x+c)**n)))**3/(h*x+g),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/172_3.4

Test file number \(172\)

Integral number in file \(312\)

Sympy [F(-2)]

Exception generated. \[ \int (a g+b g x)^m (c i+d i x)^{-2-m} \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^3 \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*g*x+a*g)**m*(d*i*x+c*i)**(-2-m)*(A+B*ln(e*((b*x+a)/(d*x+c))** 
n))**3,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/173_3.5

Test file number \(173\)

Integral number in file \(212\)

Sympy [F(-2)]

Exception generated. \[ \int (a g+b g x)^m (c i+d i x)^{-2-m} \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*g*x+a*g)**m*(d*i*x+c*i)**(-2-m)*(A+B*ln(e*((b*x+a)/(d*x+c))** 
n))**2,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/173_3.5

Test file number \(173\)

Integral number in file \(213\)

Sympy [F(-2)]

Exception generated. \[ \int (a g+b g x)^m (c i+d i x)^{-2-m} \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*g*x+a*g)**m*(d*i*x+c*i)**(-2-m)*(A+B*ln(e*((b*x+a)/(d*x+c))** 
n)),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/173_3.5

Test file number \(173\)

Integral number in file \(214\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(a g+b g x)^m (c i+d i x)^{-2-m}}{A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*g*x+a*g)**m*(d*i*x+c*i)**(-2-m)/(A+B*ln(e*((b*x+a)/(d*x+c))** 
n)),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/173_3.5

Test file number \(173\)

Integral number in file \(215\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(a g+b g x)^m (c i+d i x)^{-2-m}}{\left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*g*x+a*g)**m*(d*i*x+c*i)**(-2-m)/(A+B*ln(e*((b*x+a)/(d*x+c))** 
n))**2,x)
                                                                                    
                                                                                    
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/173_3.5

Test file number \(173\)

Integral number in file \(216\)

Sympy [F(-2)]

Exception generated. \[ \int (a g+b g x)^{-2-m} (c i+d i x)^m \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*g*x+a*g)**(-2-m)*(d*i*x+c*i)**m*(A+B*ln(e*((b*x+a)/(d*x+c))** 
n))**2,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/173_3.5

Test file number \(173\)

Integral number in file \(219\)

Sympy [F(-2)]

Exception generated. \[ \int (a g+b g x)^{-2-m} (c i+d i x)^m \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*g*x+a*g)**(-2-m)*(d*i*x+c*i)**m*(A+B*ln(e*((b*x+a)/(d*x+c))** 
n)),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/173_3.5

Test file number \(173\)

Integral number in file \(220\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(a g+b g x)^{-2-m} (c i+d i x)^m}{A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*g*x+a*g)**(-2-m)*(d*i*x+c*i)**m/(A+B*ln(e*((b*x+a)/(d*x+c))** 
n)),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/173_3.5

Test file number \(173\)

Integral number in file \(221\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(a g+b g x)^{-2-m} (c i+d i x)^m}{\left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*g*x+a*g)**(-2-m)*(d*i*x+c*i)**m/(A+B*ln(e*((b*x+a)/(d*x+c))** 
n))**2,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/173_3.5

Test file number \(173\)

Integral number in file \(222\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{(a+b x)^2} \, dx=\text {Exception raised: NotImplementedError} \] Input:

integrate(ln(e*(f*(b*x+a)**p*(d*x+c)**q)**r)/(b*x+a)**2,x)
 

Output:

Exception raised: NotImplementedError >> no valid subset found
 

input file name test_cases/rubi_tests/3_Logarithms/174_3.6

Test file number \(174\)

Integral number in file \(12\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\log \left (e \left (f (a+b x)^p (c+d x)^q\right )^r\right )}{(a+b x)^5} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(ln(e*(f*(b*x+a)**p*(d*x+c)**q)**r)/(b*x+a)**5,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/174_3.6

Test file number \(174\)

Integral number in file \(15\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\log \left (1-\frac {a+b x}{c+d x}\right )}{(a+b x) (c+d x) \log ^2\left (\frac {a+b x}{c+d x}\right )} \, dx=\text {Exception raised: TypeError} \] Input:

integrate(ln(1-(b*x+a)/(d*x+c))/(b*x+a)/(d*x+c)/ln((b*x+a)/(d*x+c))**2,x)
 

Output:

Exception raised: TypeError >> '>' not supported between instances of 'Pol 
y' and 'int'
 

input file name test_cases/rubi_tests/3_Logarithms/174_3.6

Test file number \(174\)

Integral number in file \(72\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\log \left (1-\frac {c+d x}{a+b x}\right )}{(a+b x) (c+d x) \log ^2\left (\frac {a+b x}{c+d x}\right )} \, dx=\text {Exception raised: TypeError} \] Input:

integrate(ln(1-(d*x+c)/(b*x+a))/(b*x+a)/(d*x+c)/ln((b*x+a)/(d*x+c))**2,x)
 

Output:

Exception raised: TypeError >> '>' not supported between instances of 'Pol 
y' and 'int'
 

input file name test_cases/rubi_tests/3_Logarithms/174_3.6

Test file number \(174\)

Integral number in file \(73\)

Sympy [F(-2)]

Exception generated. \[ \int \left (\frac {1}{(c+d x) (-a+c+(-b+d) x) \log \left (\frac {a+b x}{c+d x}\right )}+\frac {\log \left (1-\frac {a+b x}{c+d x}\right )}{(a+b x) (c+d x) \log ^2\left (\frac {a+b x}{c+d x}\right )}\right ) \, dx=\text {Exception raised: TypeError} \] Input:

integrate(1/(d*x+c)/(-a+c+(-b+d)*x)/ln((b*x+a)/(d*x+c))+ln(1-(b*x+a)/(d*x+ 
c))/(b*x+a)/(d*x+c)/ln((b*x+a)/(d*x+c))**2,x)
 

Output:

Exception raised: TypeError >> '>' not supported between instances of 'Pol 
y' and 'int'
 

input file name test_cases/rubi_tests/3_Logarithms/174_3.6

Test file number \(174\)

Integral number in file \(74\)

Sympy [F(-2)]

Exception generated. \[ \int \left (-\frac {1}{(a+b x) (a-c+(b-d) x) \log \left (\frac {a+b x}{c+d x}\right )}+\frac {\log \left (1-\frac {c+d x}{a+b x}\right )}{(a+b x) (c+d x) \log ^2\left (\frac {a+b x}{c+d x}\right )}\right ) \, dx=\text {Exception raised: TypeError} \] Input:

integrate(-1/(b*x+a)/(a-c+(b-d)*x)/ln((b*x+a)/(d*x+c))+ln(1-(d*x+c)/(b*x+a 
))/(b*x+a)/(d*x+c)/ln((b*x+a)/(d*x+c))**2,x)
 

Output:

Exception raised: TypeError >> '>' not supported between instances of 'Pol 
y' and 'int'
 

input file name test_cases/rubi_tests/3_Logarithms/174_3.6

Test file number \(174\)

Integral number in file \(75\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{\left (a+b \log \left (c (d+e x)^n\right )\right )^{7/2}} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(1/(a+b*ln(c*(e*x+d)**n))**(7/2),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/175_3.7

Test file number \(175\)

Integral number in file \(30\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {a+b \log \left (c (d+e x)^n\right )}{(f+g x)^4} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((a+b*ln(c*(e*x+d)**n))/(g*x+f)**4,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/175_3.7

Test file number \(175\)

Integral number in file \(43\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2}}{(f+g x)^2} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((a+b*ln(c*(e*x+d)**n))**(3/2)/(g*x+f)**2,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/175_3.7

Test file number \(175\)

Integral number in file \(115\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (a+b \log \left (c (d+e x)^n\right )\right )^{5/2}}{f+g x} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((a+b*ln(c*(e*x+d)**n))**(5/2)/(g*x+f),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/175_3.7

Test file number \(175\)

Integral number in file \(120\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{(f+g x) \left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2}} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(1/(g*x+f)/(a+b*ln(c*(e*x+d)**n))**(3/2),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
                                                                                    
                                                                                    
 

input file name test_cases/rubi_tests/3_Logarithms/175_3.7

Test file number \(175\)

Integral number in file \(132\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{(f+g x) \left (a+b \log \left (c (d+e x)^n\right )\right )^{5/2}} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(1/(g*x+f)/(a+b*ln(c*(e*x+d)**n))**(5/2),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/175_3.7

Test file number \(175\)

Integral number in file \(137\)

Sympy [F(-2)]

Exception generated. \[ \int (f+g x)^m \left (a+b \log \left (c (d+e x)^n\right )\right ) \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((g*x+f)**m*(a+b*ln(c*(e*x+d)**n)),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/175_3.7

Test file number \(175\)

Integral number in file \(162\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(f+g x)^m}{\left (a+b \log \left (c (d+e x)^n\right )\right )^2} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((g*x+f)**m/(a+b*ln(c*(e*x+d)**n))**2,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/175_3.7

Test file number \(175\)

Integral number in file \(164\)

Sympy [F(-2)]

Exception generated. \[ \int (f+g x)^m \sqrt {a+b \log \left (c (d+e x)^n\right )} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((g*x+f)**m*(a+b*ln(c*(e*x+d)**n))**(1/2),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/175_3.7

Test file number \(175\)

Integral number in file \(166\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(f+g x)^m}{\left (a+b \log \left (c (d+e x)^n\right )\right )^{3/2}} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((g*x+f)**m/(a+b*ln(c*(e*x+d)**n))**(3/2),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/175_3.7

Test file number \(175\)

Integral number in file \(168\)

Sympy [F(-2)]

Exception generated. \[ \int (f+g x)^m \left (a+b \log \left (c (d+e x)^n\right )\right )^n \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((g*x+f)**m*(a+b*ln(c*(e*x+d)**n))**n,x)
                                                                                    
                                                                                    
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/175_3.7

Test file number \(175\)

Integral number in file \(169\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {a+b \log \left (c (d+e x)^n\right )}{(d+e x) (f+g x)^{3/2}} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((a+b*ln(c*(e*x+d)**n))/(e*x+d)/(g*x+f)**(3/2),x)
 

Output:

Exception raised: TypeError >> Invalid comparison of non-real zoo
 

input file name test_cases/rubi_tests/3_Logarithms/175_3.7

Test file number \(175\)

Integral number in file \(202\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {a+b \log \left (c (d+e x)^n\right )}{(d+e x) (f+g x)^{5/2}} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((a+b*ln(c*(e*x+d)**n))/(e*x+d)/(g*x+f)**(5/2),x)
 

Output:

Exception raised: TypeError >> Invalid comparison of non-real zoo
 

input file name test_cases/rubi_tests/3_Logarithms/175_3.7

Test file number \(175\)

Integral number in file \(203\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\log \left (c \left (a-\frac {(d-a c d) x^{-m}}{c e}\right )\right )}{x \left (d+e x^m\right )} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(ln(c*(a-(-a*c*d+d)/c/e/(x**m)))/x/(d+e*x**m),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/175_3.7

Test file number \(175\)

Integral number in file \(335\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\log \left (\frac {x^{-m} \left (-d+a c d+a c e x^m\right )}{e}\right )}{x \left (d+e x^m\right )} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(ln((-d+a*c*d+a*c*e*x**m)/e/(x**m))/x/(d+e*x**m),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/175_3.7

Test file number \(175\)

Integral number in file \(336\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (\frac {e (f+g x)}{e f-d g}\right )}{d+e x} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((a+b*ln(c*(e*x+d)**n))*ln(e*(g*x+f)/(-d*g+e*f))/(e*x+d),x)
 

Output:

Exception raised: TypeError >> Invalid comparison of non-real zoo
 

input file name test_cases/rubi_tests/3_Logarithms/175_3.7

Test file number \(175\)

Integral number in file \(401\)

Sympy [F(-2)]

Exception generated. \[ \int (g+h x)^m \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right ) \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((h*x+g)**m*(a+b*ln(c*(d*(f*x+e)**p)**q)),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/175_3.7

Test file number \(175\)

Integral number in file \(525\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(g+h x)^m}{\left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^2} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((h*x+g)**m/(a+b*ln(c*(d*(f*x+e)**p)**q))**2,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/175_3.7

Test file number \(175\)

Integral number in file \(527\)

Sympy [F(-2)]

Exception generated. \[ \int (g+h x)^m \sqrt {a+b \log \left (c \left (d (e+f x)^p\right )^q\right )} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((h*x+g)**m*(a+b*ln(c*(d*(f*x+e)**p)**q))**(1/2),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/175_3.7

Test file number \(175\)

Integral number in file \(529\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(g+h x)^m}{\left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^{3/2}} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((h*x+g)**m/(a+b*ln(c*(d*(f*x+e)**p)**q))**(3/2),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/175_3.7

Test file number \(175\)

Integral number in file \(531\)

Sympy [F(-2)]

Exception generated. \[ \int (g+h x)^m \left (a+b \log \left (c \left (d (e+f x)^p\right )^q\right )\right )^n \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((h*x+g)**m*(a+b*ln(c*(d*(f*x+e)**p)**q))**n,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/175_3.7

Test file number \(175\)

Integral number in file \(532\)

Sympy [F(-2)]

Exception generated. \[ \int (f x)^{-1-n} \log \left (c \left (d+e x^n\right )^p\right ) \, dx=\text {Exception raised: TypeError} \] Input:

integrate((f*x)**(-1-n)*ln(c*(d+e*x**n)**p),x)
 

Output:

Exception raised: TypeError >> Invalid comparison of non-real zoo
 

input file name test_cases/rubi_tests/3_Logarithms/176_3.8

Test file number \(176\)

Integral number in file \(68\)

Sympy [F(-2)]

Exception generated. \[ \int (f x)^{-1-2 n} \log \left (c \left (d+e x^n\right )^p\right ) \, dx=\text {Exception raised: TypeError} \] Input:

integrate((f*x)**(-1-2*n)*ln(c*(d+e*x**n)**p),x)
 

Output:

Exception raised: TypeError >> Invalid comparison of non-real zoo
 

input file name test_cases/rubi_tests/3_Logarithms/176_3.8

Test file number \(176\)

Integral number in file \(69\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\log \left (c \left (a+b x^2\right )^p\right )}{(d+e x)^2} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(ln(c*(b*x**2+a)**p)/(e*x+d)**2,x)
 

Output:

Exception raised: AttributeError >> 'NoneType' object has no attribute 'pr 
imitive'
 

input file name test_cases/rubi_tests/3_Logarithms/176_3.8

Test file number \(176\)

Integral number in file \(189\)

Sympy [F(-2)]

Exception generated. \[ \int (d+e x)^m \log \left (c (a+b x)^p\right ) \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((e*x+d)**m*ln(c*(b*x+a)**p),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/3_Logarithms/176_3.8

Test file number \(176\)

Integral number in file \(208\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\log \left (c \left (d+e x^n\right )^p\right )}{x \left (f+g x^{-n}\right )} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(ln(c*(d+e*x**n)**p)/x/(f+g/(x**n)),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
                                                                                    
                                                                                    
 

input file name test_cases/rubi_tests/3_Logarithms/176_3.8

Test file number \(176\)

Integral number in file \(372\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\log \left (c \left (d+e x^n\right )\right )}{x \left (c e-(1-c d) x^{-n}\right )} \, dx=\text {Exception raised: TypeError} \] Input:

integrate(ln(c*(d+e*x**n))/x/(c*e-(-c*d+1)/(x**n)),x)
 

Output:

Exception raised: TypeError >> Invalid comparison of non-real zoo
 

input file name test_cases/rubi_tests/3_Logarithms/176_3.8

Test file number \(176\)

Integral number in file \(378\)