Integrals 301 to 400

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.1_Quadratic_trinomial/1.2.1.3/103_S1.6.1.f

Test file number \(103\)

Integral number in file \(412\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.1_Quadratic_trinomial/1.2.1.3/103_S1.6.1.f

Test file number \(103\)

Integral number in file \(418\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.1_Quadratic_trinomial/1.2.1.3/103_S1.6.1.f

Test file number \(103\)

Integral number in file \(427\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.1_Quadratic_trinomial/1.2.1.3/103_S1.6.1.f

Test file number \(103\)

Integral number in file \(445\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.1_Quadratic_trinomial/1.2.1.3/103_S1.6.1.f

Test file number \(103\)

Integral number in file \(446\)

Sympy [F(-2)]

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

integrate((e*x+d)**m*(g*x+f)**n,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.1_Quadratic_trinomial/1.2.1.3/103_S1.6.1.f

Test file number \(103\)

Integral number in file \(447\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.1_Quadratic_trinomial/1.2.1.3/103_S1.6.1.f

Test file number \(103\)

Integral number in file \(725\)

Sympy [F(-2)]

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

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

Output:

Exception raised: TypeError >> Invalid NaN comparison
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.1_Quadratic_trinomial/1.2.1.3/103_S1.6.1.f

Test file number \(103\)

Integral number in file \(728\)

Sympy [F(-2)]

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

integrate((e*x+d)**m/((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**m),x)
 

Output:

Exception raised: TypeError >> Invalid NaN comparison
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.1_Quadratic_trinomial/1.2.1.3/103_S1.6.1.f

Test file number \(103\)

Integral number in file \(729\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.1_Quadratic_trinomial/1.2.1.3/103_S1.6.1.f

Test file number \(103\)

Integral number in file \(730\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.1_Quadratic_trinomial/1.2.1.3/103_S1.6.1.f

Test file number \(103\)

Integral number in file \(732\)

Sympy [F(-2)]

Exception generated. \[ \int (d+e x)^m \left (c d^2 e g-e \left (c d^2+a e^2\right ) g-c d e^2 g x\right )^{-1+m} \left (a d e+\left (c d^2+a e^2\right ) x+c d e x^2\right )^{-m} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((e*x+d)**m*(c*d**2*e*g-e*(a*e**2+c*d**2)*g-c*d*e**2*g*x)**(-1+m) 
/((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**m),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.1_Quadratic_trinomial/1.2.1.3/103_S1.6.1.f

Test file number \(103\)

Integral number in file \(739\)

Sympy [F(-2)]

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

integrate((e*x+d)**m*(c*e**2*x**2+b*e**2*x+b*d*e-c*d**2)**p*((b*e-c*d)*f+( 
b*e*g-c*d*g+c*e*f)*x+c*e*g*x**2),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.1_Quadratic_trinomial/1.2.1.7/109_1.2.1.7_b

Test file number \(109\)

Integral number in file \(3\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/126_1.2.3.2_c

Test file number \(126\)

Integral number in file \(79\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (a+b \sqrt {x}+c x\right )^p}{x^3} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((a+b*x**(1/2)+c*x)**p/x**3,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
                                                                                    
                                                                                    
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/126_1.2.3.2_c

Test file number \(126\)

Integral number in file \(84\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (a+b \sqrt [3]{x}+c x^{2/3}\right )^p}{x^3} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((a+b*x**(1/3)+c*x**(2/3))**p/x**3,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/126_1.2.3.2_c

Test file number \(126\)

Integral number in file \(100\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {x^{-1-2 n}}{b x^n+c x^{2 n}} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/126_1.2.3.2_c

Test file number \(126\)

Integral number in file \(113\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/126_1.2.3.2_c

Test file number \(126\)

Integral number in file \(206\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/127_1.2.3.3_a

Test file number \(127\)

Integral number in file \(29\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/127_1.2.3.3_a

Test file number \(127\)

Integral number in file \(30\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/127_1.2.3.3_a

Test file number \(127\)

Integral number in file \(50\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {1+\left (1+\sqrt {3}\right ) x^4}{1-x^4+x^8} \, dx=\text {Exception raised: PolynomialError} \] Input:

integrate((1+(1+3**(1/2))*x**4)/(x**8-x**4+1),x)
 

Output:

Exception raised: PolynomialError >> 1/(2394670008380375980290355982690325 
81075191976715165250684200040290318941159424*_t**88 + 13825633739587334576 
2803423705330731641326126160751478072830556473063127384064*sqrt(3)*_t**88 
- 5732624312622
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/128_1.2.3.3_b

Test file number \(128\)

Integral number in file \(49\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {3-2 \sqrt {3}+\left (-3+\sqrt {3}\right ) x^4}{1-x^4+x^8} \, dx=\text {Exception raised: PolynomialError} \] Input:

integrate((3-2*3**(1/2)+(-3+3**(1/2))*x**4)/(x**8-x**4+1),x)
 

Output:

Exception raised: PolynomialError >> 1/(-36944369544063775196667969536*_t* 
*32 + 21329841701306232282053345280*sqrt(3)*_t**32 - 167111083173036783803 
087978496*sqrt(3)*_t**28 + 289444886563568182740740210688*_t**28 - 9921139 
603646460044679
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/128_1.2.3.3_b

Test file number \(128\)

Integral number in file \(50\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/128_1.2.3.3_b

Test file number \(128\)

Integral number in file \(66\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/128_1.2.3.3_b

Test file number \(128\)

Integral number in file \(67\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/128_1.2.3.3_b

Test file number \(128\)

Integral number in file \(68\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(11\)

Sympy [F(-2)]

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

integrate(x**2/(d+e*x**n)/(a+c*x**(2*n)),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(12\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(13\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(14\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(16\)

Sympy [F(-2)]

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

integrate(x**2/(d+e*x**n)**2/(a+c*x**(2*n)),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(17\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(18\)

Sympy [F(-2)]

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

integrate(x**(2*n)/(d+e*x**n)/(a+c*x**(2*n)),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(26\)

Sympy [F(-2)]

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

integrate(x**n/(d+e*x**n)/(a+c*x**(2*n)),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(27\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
                                                                                    
                                                                                    
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(28\)

Sympy [F(-2)]

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

integrate(x**(3*n)/(d+e*x**n)**2/(a+c*x**(2*n)),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(31\)

Sympy [F(-2)]

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

integrate(x**(2*n)/(d+e*x**n)**2/(a+c*x**(2*n)),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(32\)

Sympy [F(-2)]

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

integrate(x**n/(d+e*x**n)**2/(a+c*x**(2*n)),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(33\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(34\)

Sympy [F(-2)]

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

integrate(x**2*(d+e*x**n)**q/(a+c*x**(2*n)),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(52\)

Sympy [F(-2)]

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

integrate(x*(d+e*x**n)**q/(a+c*x**(2*n)),x)
                                                                                    
                                                                                    
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(53\)

Sympy [F(-2)]

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

integrate((d+e*x**n)**q/(a+c*x**(2*n)),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(54\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(61\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(135\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(139\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(140\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(141\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(142\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {1}{x^4 \left (d+e x^n\right ) \left (a+b x^n+c x^{2 n}\right )} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(1/x**4/(d+e*x**n)/(a+b*x**n+c*x**(2*n)),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(143\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(144\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(145\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(146\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(147\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(149\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(154\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
                                                                                    
                                                                                    
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(156\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(157\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(158\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(159\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(160\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(161\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(162\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(163\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(164\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(165\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(166\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(169\)

Sympy [F(-2)]

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

integrate(x**2*(d+e*x**n)**q/(a+b*x**n+c*x**(2*n)),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(174\)

Sympy [F(-2)]

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

integrate(x*(d+e*x**n)**q/(a+b*x**n+c*x**(2*n)),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(175\)

Sympy [F(-2)]

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

integrate((d+e*x**n)**q/x**2/(a+b*x**n+c*x**(2*n)),x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(178\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/131_1.2.3.4_c

Test file number \(131\)

Integral number in file \(182\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/134_1.2.3.7

Test file number \(134\)

Integral number in file \(5\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/134_1.2.3.7

Test file number \(134\)

Integral number in file \(6\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/134_1.2.3.7

Test file number \(134\)

Integral number in file \(8\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/134_1.2.3.7

Test file number \(134\)

Integral number in file \(11\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.3_General_trinomial/134_1.2.3.7

Test file number \(134\)

Integral number in file \(12\)

Sympy [F(-2)]

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

integrate((x**2+a)**(5/2)*(x+(x**2+a)**(1/2))**n,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
                                                                                    
                                                                                    
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.4_Nested_quadratic_trinomial/137_1.2.4.3

Test file number \(137\)

Integral number in file \(26\)

Sympy [F(-2)]

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

integrate((x**2+a)**(5/2)*(x-(x**2+a)**(1/2))**n,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.4_Nested_quadratic_trinomial/137_1.2.4.3

Test file number \(137\)

Integral number in file \(32\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.4_Nested_quadratic_trinomial/137_1.2.4.3

Test file number \(137\)

Integral number in file \(45\)

Sympy [F(-2)]

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

integrate((a+2*d*e*x/f**2+e**2*x**2/f**2)**(1/2)*(d+e*x+f*(a+2*d*e*x/f**2+ 
e**2*x**2/f**2)**(1/2))**n,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.4_Nested_quadratic_trinomial/137_1.2.4.3

Test file number \(137\)

Integral number in file \(46\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.4_Nested_quadratic_trinomial/137_1.2.4.3

Test file number \(137\)

Integral number in file \(48\)

Sympy [F(-2)]

Exception generated. \[ \int \left (1-(1-6 b)^{3/2}-9 b+54 b x-54 x^2+108 x^3\right )^p \, dx=\text {Exception raised: AttributeError} \] Input:

integrate((1-(1-6*b)**(3/2)-9*b+54*b*x-54*x**2+108*x**3)**p,x)
 

Output:

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

input file name test_cases/rubi_tests/1_Algebraic_functions/1.3_Cubic/142_1.3.1

Test file number \(142\)

Integral number in file \(85\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {b e+2 c e x+3 d e x^2}{\left (a+b x+c x^2+d x^3\right )^{5/2}} \, dx=\text {Exception raised: RecursionError} \] Input:

integrate((3*d*e*x**2+2*c*e*x+b*e)/(d*x**3+c*x**2+b*x+a)**(5/2),x)
                                                                                    
                                                                                    
 

Output:

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

input file name test_cases/rubi_tests/1_Algebraic_functions/1.3_Cubic/143_1.3.2

Test file number \(143\)

Integral number in file \(107\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (3-2 \sqrt {2}+x^2\right )^2 \left (-3+2 \sqrt {2}+x^2\right )}{577-408 \sqrt {2}-8 \left (-41+29 \sqrt {2}\right ) x^2-2 \left (-39+28 \sqrt {2}\right ) x^4-8 \left (-1+\sqrt {2}\right ) x^6+x^8} \, dx=\text {Exception raised: PolynomialError} \] Input:

integrate((3-2*2**(1/2)+x**2)**2*(-3+2*2**(1/2)+x**2)/(577-408*2**(1/2)-8* 
(-41+29*2**(1/2))*x**2-2*(-39+28*2**(1/2))*x**4-8*(2**(1/2)-1)*x**6+x**8), 
x)
 

Output:

Exception raised: PolynomialError >> 1/(-489331912114255602061892417478047 
2498117708482611714912381696*_t**4 + 3460099133069698398004476359279702930 
052248019321310378430976*sqrt(2)*_t**4 - 159769239484575670917838951113184 
628965915778476
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.5_Polynomial/147_1.7.2

Test file number \(147\)

Integral number in file \(70\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {-3+2 \sqrt {2}+x^2}{17-12 \sqrt {2}+\left (2-4 \sqrt {2}\right ) x^2+x^4} \, dx=\text {Exception raised: PolynomialError} \] Input:

integrate((-3+2*2**(1/2)+x**2)/(17-12*2**(1/2)+(2-4*2**(1/2))*x**2+x**4),x 
)
 

Output:

Exception raised: PolynomialError >> 1/(-2304*_t**4 + 1024*sqrt(2)*_t**4 - 
 32*_t**2 + 64*sqrt(2)*_t**2 - 1) contains an element of the set of genera 
tors.
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.5_Polynomial/147_1.7.2

Test file number \(147\)

Integral number in file \(97\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (-3+2 \sqrt {2}\right )^2-x^4}{-99+70 \sqrt {2}+\left (-39+28 \sqrt {2}\right ) x^2+\left (-5+6 \sqrt {2}\right ) x^4-x^6} \, dx=\text {Exception raised: PolynomialError} \] Input:

integrate(((-3+2*2**(1/2))**2-x**4)/(-99+70*2**(1/2)+(-39+28*2**(1/2))*x** 
2+(-5+6*2**(1/2))*x**4-x**6),x)
 

Output:

Exception raised: PolynomialError >> 1/(-160817378869521623700434126076296 
32108508413135104*_t**4 + 113715059131284938253449200806460980121432594954 
24*sqrt(2)*_t**4 - 525076531527889516631004780624192141786868300832*_t**2 
+ 3712851760852
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.5_Polynomial/147_1.7.2

Test file number \(147\)

Integral number in file \(98\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (-3+2 \sqrt {2}-x^2\right ) \left (-3+2 \sqrt {2}+x^2\right )}{-99+70 \sqrt {2}+\left (-39+28 \sqrt {2}\right ) x^2+\left (-5+6 \sqrt {2}\right ) x^4-x^6} \, dx=\text {Exception raised: PolynomialError} \] Input:

integrate((-3+2*2**(1/2)-x**2)*(-3+2*2**(1/2)+x**2)/(-99+70*2**(1/2)+(-39+ 
28*2**(1/2))*x**2+(-5+6*2**(1/2))*x**4-x**6),x)
 

Output:

Exception raised: PolynomialError >> 1/(-160817378869521623700434126076296 
32108508413135104*_t**4 + 113715059131284938253449200806460980121432594954 
24*sqrt(2)*_t**4 - 525076531527889516631004780624192141786868300832*_t**2 
+ 3712851760852
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.5_Polynomial/147_1.7.2

Test file number \(147\)

Integral number in file \(99\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (-3+2 \sqrt {2}\right )^3-\left (-3+2 \sqrt {2}\right )^2 x^2-\left (-3+2 \sqrt {2}\right ) x^4+x^6}{577-408 \sqrt {2}+\left (328-232 \sqrt {2}\right ) x^2+\left (78-56 \sqrt {2}\right ) x^4+\left (8-8 \sqrt {2}\right ) x^6+x^8} \, dx=\text {Exception raised: PolynomialError} \] Input:

integrate(((-3+2*2**(1/2))**3-(-3+2*2**(1/2))**2*x**2-(-3+2*2**(1/2))*x**4 
+x**6)/(577-408*2**(1/2)+(328-232*2**(1/2))*x**2+(78-56*2**(1/2))*x**4+(8- 
8*2**(1/2))*x**6+x**8),x)
 

Output:

Exception raised: PolynomialError >> 1/(-489331912114255602061892417478047 
2498117708482611714912381696*_t**4 + 3460099133069698398004476359279702930 
052248019321310378430976*sqrt(2)*_t**4 - 159769239484575670917838951113184 
628965915778476
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.5_Polynomial/147_1.7.2

Test file number \(147\)

Integral number in file \(100\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (3-2 \sqrt {2}+x^2\right )^2 \left (-3+2 \sqrt {2}+x^2\right )}{577-408 \sqrt {2}+\left (328-232 \sqrt {2}\right ) x^2+\left (78-56 \sqrt {2}\right ) x^4+\left (8-8 \sqrt {2}\right ) x^6+x^8} \, dx=\text {Exception raised: PolynomialError} \] Input:

integrate((3-2*2**(1/2)+x**2)**2*(-3+2*2**(1/2)+x**2)/(577-408*2**(1/2)+(3 
28-232*2**(1/2))*x**2+(78-56*2**(1/2))*x**4+(8-8*2**(1/2))*x**6+x**8),x)
 

Output:

Exception raised: PolynomialError >> 1/(-489331912114255602061892417478047 
2498117708482611714912381696*_t**4 + 3460099133069698398004476359279702930 
052248019321310378430976*sqrt(2)*_t**4 - 159769239484575670917838951113184 
628965915778476
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.5_Polynomial/147_1.7.2

Test file number \(147\)

Integral number in file \(101\)

Sympy [F(-2)]

Exception generated. \[ \int \sqrt {\frac {1}{x}} \sqrt {x} \sqrt {a+b x} \, dx=\text {Exception raised: RecursionError} \] Input:

integrate((1/x)**(1/2)*x**(1/2)*(b*x+a)**(1/2),x)
 

Output:

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

input file name test_cases/rubi_tests/1_Algebraic_functions/1.6_Miscellaneous/149_1.6.1

Test file number \(149\)

Integral number in file \(469\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\sqrt {-1+\frac {1}{x}} \sqrt {\frac {1}{x}} \sqrt {x}}{\sqrt {1+x}} \, dx=\text {Exception raised: RecursionError} \] Input:

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

Output:

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

input file name test_cases/rubi_tests/1_Algebraic_functions/1.6_Miscellaneous/149_1.6.1

Test file number \(149\)

Integral number in file \(536\)

Sympy [F(-2)]

Exception generated. \[ \int x^5 \left (c+d x^2+e \sqrt {a+b x^2}\right )^p \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate(x**5*(c+d*x**2+e*(b*x**2+a)**(1/2))**p,x)
 

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.6_Miscellaneous/152_1.6.5

Test file number \(152\)

Integral number in file \(23\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.6_Miscellaneous/152_1.6.5

Test file number \(152\)

Integral number in file \(24\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.6_Miscellaneous/152_1.6.5

Test file number \(152\)

Integral number in file \(27\)

Sympy [F(-2)]

Exception generated. \[ \int a^x b^{-x} \, dx=\text {Exception raised: TypeError} \] Input:

integrate(a**x/(b**x),x)
 

Output:

Exception raised: TypeError >> Invalid NaN comparison
 

input file name test_cases/rubi_tests/2_Exponentials/155_2_Exponential_functions

Test file number \(155\)

Integral number in file \(491\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/2_Exponentials/155_2_Exponential_functions

Test file number \(155\)

Integral number in file \(517\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck
 

input file name test_cases/rubi_tests/2_Exponentials/155_2_Exponential_functions

Test file number \(155\)

Integral number in file \(532\)

Sympy [F(-2)]

Exception generated. \[ \int 2^{2+3 x} 3^{5+7 x} \, dx=\text {Exception raised: IndexError} \] Input:

integrate(2**(2+3*x)*3**(5+7*x),x)
 

Output:

Exception raised: IndexError >> Index out of range: a[1]
                                                                                    
                                                                                    
 

input file name test_cases/rubi_tests/2_Exponentials/155_2_Exponential_functions

Test file number \(155\)

Integral number in file \(707\)

Sympy [F(-2)]

Exception generated. \[ \int 2^{2+3 x} 3^{5+7 x} 5^{11+13 x} \, dx=\text {Exception raised: IndexError} \] Input:

integrate(2**(2+3*x)*3**(5+7*x)*5**(11+13*x),x)
 

Output:

Exception raised: IndexError >> Index out of range: a[1]
 

input file name test_cases/rubi_tests/2_Exponentials/155_2_Exponential_functions

Test file number \(155\)

Integral number in file \(710\)