Integrals 501 to 600

Sympy [F(-2)]

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

integrate(x**(-1+n)*ln(c*(d+e*x**n))/(-1+c*d+c*e*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 \(379\)

Sympy [F(-2)]

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

integrate((f+g*x**n)**2*ln(c*(d+e*x**n)**p)**q/x,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 \(382\)

Sympy [F(-2)]

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

integrate((f+g/(x**n))**2*ln(c*(d+e*x**n)**p)**q/x,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 \(383\)

Sympy [F(-2)]

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

integrate(ln(c*(d+e*x**n)**p)**q/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 \(387\)

Sympy [F(-2)]

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

integrate(ln(x)*ln(d+e*x**m)/x,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 \(389\)

Sympy [F(-2)]

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

integrate((g*x+f)*(a+b*ln(c*(e*x**2+d)**p))/(h*x)**(1/2),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 \(606\)

Sympy [F(-2)]

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

integrate((g*x+f)*(a+b*ln(c*(e*x**2+d)**p))/(h*x)**(3/2),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 \(607\)

Sympy [F(-2)]

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

integrate((g*x+f)*(a+b*ln(c*(e*x**2+d)**p))/(h*x)**(5/2),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 \(608\)

Sympy [F(-2)]

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

integrate((g*x+f)**2*(a+b*ln(c*(e*x**2+d)**p))/(h*x)**(1/2),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 \(611\)

Sympy [F(-2)]

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

integrate((g*x+f)**2*(a+b*ln(c*(e*x**2+d)**p))/(h*x)**(3/2),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 \(612\)

Sympy [F(-2)]

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

integrate((g*x+f)**2*(a+b*ln(c*(e*x**2+d)**p))/(h*x)**(5/2),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 \(613\)

Sympy [F(-2)]

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

integrate(ln(f*x**p)*ln(1+e*x**m)/x,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 \(619\)

Sympy [F(-2)]

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

integrate(ln(f*x**p)*(a+b*ln(c*(d+e*x**m)**n))/x,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 \(623\)

Sympy [F(-2)]

Exception generated. \[ \int \sec ^4(c+d x) (a+b \sin (c+d x))^m \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(sec(d*x+c)**4*(a+b*sin(d*x+c))**m,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/4_Trig_functions/4.1_Sine/180_4.1.1.2

Test file number \(180\)

Integral number in file \(634\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
                                                                                    
                                                                                    
 

input file name test_cases/rubi_tests/4_Trig_functions/4.1_Sine/182_4.1.2.1

Test file number \(182\)

Integral number in file \(808\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(g \cos (e+f x))^{3/2} (a+a \sin (e+f x))^m}{(c-c \sin (e+f x))^3} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**m/(c-c*sin(f*x+e))**3,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/4_Trig_functions/4.1_Sine/183_4.1.2.2

Test file number \(183\)

Integral number in file \(158\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\cos ^4(e+f x) (c+d \sin (e+f x))^n}{(a+a \sin (e+f x))^2} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(cos(f*x+e)**4*(c+d*sin(f*x+e))**n/(a+a*sin(f*x+e))**2,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/4_Trig_functions/4.1_Sine/183_4.1.2.2

Test file number \(183\)

Integral number in file \(946\)

Sympy [F(-2)]

Exception generated. \[ \int \sec ^4(e+f x) (a+a \sin (e+f x))^m (A+B \sin (e+f x)) \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(sec(f*x+e)**4*(a+a*sin(f*x+e))**m*(A+B*sin(f*x+e)),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/4_Trig_functions/4.1_Sine/183_4.1.2.2

Test file number \(183\)

Integral number in file \(1027\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/4_Trig_functions/4.1_Sine/183_4.1.2.2

Test file number \(183\)

Integral number in file \(1517\)

Sympy [F(-2)]

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

integrate(cos(f*x+e)**2*(c+d*sin(f*x+e))**n/(a+b*sin(f*x+e))**2,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/4_Trig_functions/4.1_Sine/183_4.1.2.2

Test file number \(183\)

Integral number in file \(1523\)

Sympy [F(-2)]

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

integrate((a+b*sin(f*x+e))**m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))**n,x)
                                                                                    
                                                                                    
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/4_Trig_functions/4.1_Sine/185_4.1.3.1

Test file number \(185\)

Integral number in file \(358\)

Sympy [F(-2)]

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

integrate((a+b*sin(f*x+e))**m*(c+d*sin(f*x+e))**n*(A+B*sin(f*x+e)+C*sin(f* 
x+e)**2),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/4_Trig_functions/4.1_Sine/187_4.1.4.2

Test file number \(187\)

Integral number in file \(32\)

Sympy [F(-2)]

Exception generated. \[ \int \cos ^5(e+f x) \left (a+b \sin ^n(e+f x)\right )^p \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(cos(f*x+e)**5*(a+b*sin(f*x+e)**n)**p,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/4_Trig_functions/4.1_Sine/189_4.1.7.2

Test file number \(189\)

Integral number in file \(362\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\sin ^3(c+d x)}{(e+f x) (a+a \sin (c+d x))} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(sin(d*x+c)**3/(f*x+e)/(a+a*sin(d*x+c)),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/4_Trig_functions/4.1_Sine/192_4.1.10

Test file number \(192\)

Integral number in file \(195\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\cos ^3(c+d x)}{(e+f x) (a+a \sin (c+d x))} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(cos(d*x+c)**3/(f*x+e)/(a+a*sin(d*x+c)),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/4_Trig_functions/4.1_Sine/192_4.1.10

Test file number \(192\)

Integral number in file \(267\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(e+f x)^m \cos ^4(c+d x)}{a+a \sin (c+d x)} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((f*x+e)**m*cos(d*x+c)**4/(a+a*sin(d*x+c)),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/4_Trig_functions/4.1_Sine/192_4.1.10

Test file number \(192\)

Integral number in file \(287\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(e+f x)^m \cos ^3(c+d x)}{a+a \sin (c+d x)} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((f*x+e)**m*cos(d*x+c)**3/(a+a*sin(d*x+c)),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/4_Trig_functions/4.1_Sine/192_4.1.10

Test file number \(192\)

Integral number in file \(288\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\cos ^2(c+d x)}{(a+b \tan (c+d x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(cos(d*x+c)**2/(a+b*tan(d*x+c))**3,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/215_4.3.1.2

Test file number \(215\)

Integral number in file \(578\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\cos ^4(c+d x)}{(a+b \tan (c+d x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(cos(d*x+c)**4/(a+b*tan(d*x+c))**3,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/215_4.3.1.2

Test file number \(215\)

Integral number in file \(579\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\sin ^6(c+d x)}{(a+b \tan (c+d x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(sin(d*x+c)**6/(a+b*tan(d*x+c))**3,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/216_4.3.1.3

Test file number \(216\)

Integral number in file \(67\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\sin ^4(c+d x)}{(a+b \tan (c+d x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(sin(d*x+c)**4/(a+b*tan(d*x+c))**3,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/216_4.3.1.3

Test file number \(216\)

Integral number in file \(68\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\sin ^2(c+d x)}{(a+b \tan (c+d x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(sin(d*x+c)**2/(a+b*tan(d*x+c))**3,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/216_4.3.1.3

Test file number \(216\)

Integral number in file \(69\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\sin ^4(c+d x)}{(a+b \tan (c+d x))^4} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(sin(d*x+c)**4/(a+b*tan(d*x+c))**4,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/216_4.3.1.3

Test file number \(216\)

Integral number in file \(73\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\sin ^2(c+d x)}{(a+b \tan (c+d x))^4} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(sin(d*x+c)**2/(a+b*tan(d*x+c))**4,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/216_4.3.1.3

Test file number \(216\)

Integral number in file \(74\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\tan ^6(c+d x)}{(a+b \tan (c+d x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(tan(d*x+c)**6/(a+b*tan(d*x+c))**3,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/217_4.3.2.1

Test file number \(217\)

Integral number in file \(477\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\tan ^5(c+d x)}{(a+b \tan (c+d x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(tan(d*x+c)**5/(a+b*tan(d*x+c))**3,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/217_4.3.2.1

Test file number \(217\)

Integral number in file \(478\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\tan ^4(c+d x)}{(a+b \tan (c+d x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(tan(d*x+c)**4/(a+b*tan(d*x+c))**3,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/217_4.3.2.1

Test file number \(217\)

Integral number in file \(479\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\tan ^3(c+d x)}{(a+b \tan (c+d x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(tan(d*x+c)**3/(a+b*tan(d*x+c))**3,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/217_4.3.2.1

Test file number \(217\)

Integral number in file \(480\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\tan ^2(c+d x)}{(a+b \tan (c+d x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(tan(d*x+c)**2/(a+b*tan(d*x+c))**3,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/217_4.3.2.1

Test file number \(217\)

Integral number in file \(481\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\tan (c+d x)}{(a+b \tan (c+d x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(tan(d*x+c)/(a+b*tan(d*x+c))**3,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/217_4.3.2.1

Test file number \(217\)

Integral number in file \(482\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{(a+b \tan (c+d x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(1/(a+b*tan(d*x+c))**3,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/217_4.3.2.1

Test file number \(217\)

Integral number in file \(483\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\cot (c+d x)}{(a+b \tan (c+d x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(cot(d*x+c)/(a+b*tan(d*x+c))**3,x)
                                                                                    
                                                                                    
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/217_4.3.2.1

Test file number \(217\)

Integral number in file \(484\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\cot ^2(c+d x)}{(a+b \tan (c+d x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(cot(d*x+c)**2/(a+b*tan(d*x+c))**3,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/217_4.3.2.1

Test file number \(217\)

Integral number in file \(485\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\tan ^6(c+d x)}{(a+b \tan (c+d x))^4} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(tan(d*x+c)**6/(a+b*tan(d*x+c))**4,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/217_4.3.2.1

Test file number \(217\)

Integral number in file \(486\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\tan ^5(c+d x)}{(a+b \tan (c+d x))^4} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(tan(d*x+c)**5/(a+b*tan(d*x+c))**4,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/217_4.3.2.1

Test file number \(217\)

Integral number in file \(487\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\tan ^4(c+d x)}{(a+b \tan (c+d x))^4} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(tan(d*x+c)**4/(a+b*tan(d*x+c))**4,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/217_4.3.2.1

Test file number \(217\)

Integral number in file \(488\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\tan ^3(c+d x)}{(a+b \tan (c+d x))^4} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(tan(d*x+c)**3/(a+b*tan(d*x+c))**4,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/217_4.3.2.1

Test file number \(217\)

Integral number in file \(489\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\tan ^2(c+d x)}{(a+b \tan (c+d x))^4} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(tan(d*x+c)**2/(a+b*tan(d*x+c))**4,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/217_4.3.2.1

Test file number \(217\)

Integral number in file \(490\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\tan (c+d x)}{(a+b \tan (c+d x))^4} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(tan(d*x+c)/(a+b*tan(d*x+c))**4,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/217_4.3.2.1

Test file number \(217\)

Integral number in file \(491\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{(a+b \tan (c+d x))^4} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(1/(a+b*tan(d*x+c))**4,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/217_4.3.2.1

Test file number \(217\)

Integral number in file \(492\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\cot (c+d x)}{(a+b \tan (c+d x))^4} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(cot(d*x+c)/(a+b*tan(d*x+c))**4,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/217_4.3.2.1

Test file number \(217\)

Integral number in file \(493\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\cot ^2(c+d x)}{(a+b \tan (c+d x))^4} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(cot(d*x+c)**2/(a+b*tan(d*x+c))**4,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/217_4.3.2.1

Test file number \(217\)

Integral number in file \(494\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {c+d \tan (e+f x)}{(a+b \tan (e+f x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate((c+d*tan(f*x+e))/(a+b*tan(f*x+e))**3,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/217_4.3.2.1

Test file number \(217\)

Integral number in file \(1196\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(c+d \tan (e+f x))^2}{(a+b \tan (e+f x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

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

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/217_4.3.2.1

Test file number \(217\)

Integral number in file \(1202\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(c+d \tan (e+f x))^3}{(a+b \tan (e+f x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate((c+d*tan(f*x+e))**3/(a+b*tan(f*x+e))**3,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/217_4.3.2.1

Test file number \(217\)

Integral number in file \(1208\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{(a+b \tan (e+f x))^2 (c+d \tan (e+f x))} \, dx=\text {Exception raised: NotImplementedError} \] Input:

integrate(1/(a+b*tan(f*x+e))**2/(c+d*tan(f*x+e)),x)
 

Output:

Exception raised: NotImplementedError >> no valid subset found
 

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/217_4.3.2.1

Test file number \(217\)

Integral number in file \(1214\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{(a+b \tan (e+f x))^3 (c+d \tan (e+f x))} \, dx=\text {Exception raised: NotImplementedError} \] Input:

integrate(1/(a+b*tan(f*x+e))**3/(c+d*tan(f*x+e)),x)
 

Output:

Exception raised: NotImplementedError >> no valid subset found
                                                                                    
                                                                                    
 

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/217_4.3.2.1

Test file number \(217\)

Integral number in file \(1215\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{(a+b \tan (e+f x)) (c+d \tan (e+f x))^2} \, dx=\text {Exception raised: NotImplementedError} \] Input:

integrate(1/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))**2,x)
 

Output:

Exception raised: NotImplementedError >> no valid subset found
 

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/217_4.3.2.1

Test file number \(217\)

Integral number in file \(1220\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{(a+b \tan (e+f x))^2 (c+d \tan (e+f x))^2} \, dx=\text {Exception raised: NotImplementedError} \] Input:

integrate(1/(a+b*tan(f*x+e))**2/(c+d*tan(f*x+e))**2,x)
 

Output:

Exception raised: NotImplementedError >> no valid subset found
 

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/217_4.3.2.1

Test file number \(217\)

Integral number in file \(1221\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{(a+b \tan (e+f x))^3 (c+d \tan (e+f x))^2} \, dx=\text {Exception raised: NotImplementedError} \] Input:

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

Output:

Exception raised: NotImplementedError >> no valid subset found
 

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/217_4.3.2.1

Test file number \(217\)

Integral number in file \(1222\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(a+b \tan (e+f x))^4}{(c+d \tan (e+f x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate((a+b*tan(f*x+e))**4/(c+d*tan(f*x+e))**3,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/217_4.3.2.1

Test file number \(217\)

Integral number in file \(1223\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(a+b \tan (e+f x))^3}{(c+d \tan (e+f x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate((a+b*tan(f*x+e))**3/(c+d*tan(f*x+e))**3,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/217_4.3.2.1

Test file number \(217\)

Integral number in file \(1224\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(a+b \tan (e+f x))^2}{(c+d \tan (e+f x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

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

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/217_4.3.2.1

Test file number \(217\)

Integral number in file \(1225\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {a+b \tan (e+f x)}{(c+d \tan (e+f x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate((a+b*tan(f*x+e))/(c+d*tan(f*x+e))**3,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/217_4.3.2.1

Test file number \(217\)

Integral number in file \(1226\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{(a+b \tan (e+f x)) (c+d \tan (e+f x))^3} \, dx=\text {Exception raised: NotImplementedError} \] Input:

integrate(1/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))**3,x)
 

Output:

Exception raised: NotImplementedError >> no valid subset found
 

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/217_4.3.2.1

Test file number \(217\)

Integral number in file \(1227\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{(a+b \tan (e+f x))^2 (c+d \tan (e+f x))^3} \, dx=\text {Exception raised: NotImplementedError} \] Input:

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

Output:

Exception raised: NotImplementedError >> no valid subset found
 

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/217_4.3.2.1

Test file number \(217\)

Integral number in file \(1228\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/217_4.3.2.1

Test file number \(217\)

Integral number in file \(1320\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {A+B \tan (c+d x)}{\sqrt {\tan (c+d x)} (a+i a \tan (c+d x))} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((A+B*tan(d*x+c))/tan(d*x+c)**(1/2)/(a+I*a*tan(d*x+c)),x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/218_4.3.3.1

Test file number \(218\)

Integral number in file \(137\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {A+B \tan (c+d x)}{\tan ^{\frac {3}{2}}(c+d x) (a+i a \tan (c+d x))} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((A+B*tan(d*x+c))/tan(d*x+c)**(3/2)/(a+I*a*tan(d*x+c)),x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/218_4.3.3.1

Test file number \(218\)

Integral number in file \(138\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {A+B \tan (c+d x)}{\sqrt {\tan (c+d x)} (a+i a \tan (c+d x))^2} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((A+B*tan(d*x+c))/tan(d*x+c)**(1/2)/(a+I*a*tan(d*x+c))**2,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/218_4.3.3.1

Test file number \(218\)

Integral number in file \(143\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {A+B \tan (c+d x)}{\tan ^{\frac {3}{2}}(c+d x) (a+i a \tan (c+d x))^2} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((A+B*tan(d*x+c))/tan(d*x+c)**(3/2)/(a+I*a*tan(d*x+c))**2,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/218_4.3.3.1

Test file number \(218\)

Integral number in file \(144\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {A+B \tan (c+d x)}{\sqrt {\tan (c+d x)} (a+i a \tan (c+d x))^3} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((A+B*tan(d*x+c))/tan(d*x+c)**(1/2)/(a+I*a*tan(d*x+c))**3,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/218_4.3.3.1

Test file number \(218\)

Integral number in file \(151\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {A+B \tan (c+d x)}{\tan ^{\frac {3}{2}}(c+d x) (a+i a \tan (c+d x))^3} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((A+B*tan(d*x+c))/tan(d*x+c)**(3/2)/(a+I*a*tan(d*x+c))**3,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/218_4.3.3.1

Test file number \(218\)

Integral number in file \(152\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\tan ^4(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(tan(d*x+c)**4*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**3,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/218_4.3.3.1

Test file number \(218\)

Integral number in file \(282\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\tan ^3(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(tan(d*x+c)**3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**3,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/218_4.3.3.1

Test file number \(218\)

Integral number in file \(283\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\tan ^2(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

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

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/218_4.3.3.1

Test file number \(218\)

Integral number in file \(284\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\tan (c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**3,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/218_4.3.3.1

Test file number \(218\)

Integral number in file \(285\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {A+B \tan (c+d x)}{(a+b \tan (c+d x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c))**3,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/218_4.3.3.1

Test file number \(218\)

Integral number in file \(286\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\cot (c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**3,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/218_4.3.3.1

Test file number \(218\)

Integral number in file \(287\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\cot ^2(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(cot(d*x+c)**2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**3,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/218_4.3.3.1

Test file number \(218\)

Integral number in file \(288\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\cot ^3(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(cot(d*x+c)**3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**3,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/218_4.3.3.1

Test file number \(218\)

Integral number in file \(289\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\tan ^4(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^4} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(tan(d*x+c)**4*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**4,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/218_4.3.3.1

Test file number \(218\)

Integral number in file \(290\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\tan ^3(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^4} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(tan(d*x+c)**3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**4,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/218_4.3.3.1

Test file number \(218\)

Integral number in file \(291\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\tan ^2(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^4} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(tan(d*x+c)**2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**4,x)
                                                                                    
                                                                                    
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/218_4.3.3.1

Test file number \(218\)

Integral number in file \(292\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\tan (c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^4} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**4,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/218_4.3.3.1

Test file number \(218\)

Integral number in file \(293\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {A+B \tan (c+d x)}{(a+b \tan (c+d x))^4} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c))**4,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/218_4.3.3.1

Test file number \(218\)

Integral number in file \(294\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\cot (c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^4} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**4,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/218_4.3.3.1

Test file number \(218\)

Integral number in file \(295\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\cot ^2(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^4} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(cot(d*x+c)**2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**4,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/218_4.3.3.1

Test file number \(218\)

Integral number in file \(296\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\cot ^3(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^4} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(cot(d*x+c)**3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**4,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/218_4.3.3.1

Test file number \(218\)

Integral number in file \(297\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\tan ^3(c+d x) \left (B \tan (c+d x)+C \tan ^2(c+d x)\right )}{(a+b \tan (c+d x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(tan(d*x+c)**3*(B*tan(d*x+c)+C*tan(d*x+c)**2)/(a+b*tan(d*x+c))**3 
,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/219_4.3.4.2

Test file number \(219\)

Integral number in file \(38\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\tan ^2(c+d x) \left (B \tan (c+d x)+C \tan ^2(c+d x)\right )}{(a+b \tan (c+d x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(tan(d*x+c)**2*(B*tan(d*x+c)+C*tan(d*x+c)**2)/(a+b*tan(d*x+c))**3 
,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/219_4.3.4.2

Test file number \(219\)

Integral number in file \(39\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\tan (c+d x) \left (B \tan (c+d x)+C \tan ^2(c+d x)\right )}{(a+b \tan (c+d x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(tan(d*x+c)*(B*tan(d*x+c)+C*tan(d*x+c)**2)/(a+b*tan(d*x+c))**3,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/219_4.3.4.2

Test file number \(219\)

Integral number in file \(40\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {B \tan (c+d x)+C \tan ^2(c+d x)}{(a+b \tan (c+d x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate((B*tan(d*x+c)+C*tan(d*x+c)**2)/(a+b*tan(d*x+c))**3,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/219_4.3.4.2

Test file number \(219\)

Integral number in file \(41\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\cot (c+d x) \left (B \tan (c+d x)+C \tan ^2(c+d x)\right )}{(a+b \tan (c+d x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(cot(d*x+c)*(B*tan(d*x+c)+C*tan(d*x+c)**2)/(a+b*tan(d*x+c))**3,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/219_4.3.4.2

Test file number \(219\)

Integral number in file \(42\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\cot ^2(c+d x) \left (B \tan (c+d x)+C \tan ^2(c+d x)\right )}{(a+b \tan (c+d x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(cot(d*x+c)**2*(B*tan(d*x+c)+C*tan(d*x+c)**2)/(a+b*tan(d*x+c))**3 
,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/219_4.3.4.2

Test file number \(219\)

Integral number in file \(43\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\cot ^3(c+d x) \left (B \tan (c+d x)+C \tan ^2(c+d x)\right )}{(a+b \tan (c+d x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate(cot(d*x+c)**3*(B*tan(d*x+c)+C*tan(d*x+c)**2)/(a+b*tan(d*x+c))**3 
,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/219_4.3.4.2

Test file number \(219\)

Integral number in file \(44\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(c+d \tan (e+f x)) \left (A+B \tan (e+f x)+C \tan ^2(e+f x)\right )}{(a+b \tan (e+f x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate((c+d*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e 
))**3,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/219_4.3.4.2

Test file number \(219\)

Integral number in file \(56\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(c+d \tan (e+f x))^2 \left (A+B \tan (e+f x)+C \tan ^2(e+f x)\right )}{(a+b \tan (e+f x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate((c+d*tan(f*x+e))**2*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f* 
x+e))**3,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/219_4.3.4.2

Test file number \(219\)

Integral number in file \(63\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(c+d \tan (e+f x))^3 \left (A+B \tan (e+f x)+C \tan ^2(e+f x)\right )}{(a+b \tan (e+f x))^3} \, dx=\text {Exception raised: AttributeError} \] Input:

integrate((c+d*tan(f*x+e))**3*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f* 
x+e))**3,x)
 

Output:

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

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/219_4.3.4.2

Test file number \(219\)

Integral number in file \(69\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^2 (c+d \tan (e+f x))} \, dx=\text {Exception raised: NotImplementedError} \] Input:

integrate((A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**2/(c+d*tan(f* 
x+e)),x)
 

Output:

Exception raised: NotImplementedError >> no valid subset found
 

input file name test_cases/rubi_tests/4_Trig_functions/4.3_Tangent/219_4.3.4.2

Test file number \(219\)

Integral number in file \(75\)