Integrals 301 to 400

Sympy [F(-2)]

Exception generated. $$\int \frac{(d+ex{)}^m(a+bx+c{x}^2)}{(f+gx{)}^2}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{(d+ex{)}^m{(a+bx+c{x}^2)}^2}{(f+gx{)}^2}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{(f+gx{)}^n(a+2cdx+ce{x}^2)}{(d+ex{)}^2}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int (d+ex{)}^m(f+gx{)}^n{(a+bx+c{x}^2)}^{2}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int (d+ex{)}^m(f+gx{)}^n(a+bx+c{x}^2)dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int (d+ex{)}^m(f+gx{)}^{n}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int (d+ex{)}^m(f+gx{)}^n{(ade+(c{d}^2+a{e}^2)x+cde{x}^2)}^{-m}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int (d+ex{)}^m(f+gx){(ade+(c{d}^2+a{e}^2)x+cde{x}^2)}^{-m}dx=\text{Exception raised: TypeError}$$ 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. $$\int (d+ex{)}^m{(ade+(c{d}^2+a{e}^2)x+cde{x}^2)}^{-m}dx=\text{Exception raised: TypeError}$$ 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. $$\int \frac{(d+ex{)}^m{(ade+(c{d}^2+a{e}^2)x+cde{x}^2)}^{-m}}{f+gx}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{(d+ex{)}^m{(ade+(c{d}^2+a{e}^2)x+cde{x}^2)}^{-m}}{(f+gx{)}^3}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int (d+ex{)}^m{(c{d}^{2}eg-e(c{d}^2+a{e}^2)g-cd{e}^{2}gx)}^{-1+m}{(ade+(c{d}^2+a{e}^2)x+cde{x}^2)}^{-m}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int (d+ex{)}^m{(-c{d}^2+bde+b{e}^{2}x+c{e}^2{x}^2)}^p((-cd+be)f+(cef-cdg+beg)x+ceg{x}^2)dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int x^2{(a+b\sqrt{x}+cx)}^{p}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{{(a+b\sqrt{x}+cx)}^p}{x^3}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{{(a+b\sqrt[3]{x}+c{x}^{2/3})}^p}{x^3}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{x^{-1-2n}}{b{x}^n+c{x}^{2n}}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{1}{(dx{)}^{5/2}(a+b{x}^n+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{1}{(d+e{x}^n)(a+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{1}{{(d+e{x}^n)}^2(a+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{{(a+c{x}^{2n})}^p}{d+e{x}^n}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{1+(1+\sqrt{3})x^4}{1-x^4+x^8}dx=\text{Exception raised: PolynomialError}$$ 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. $$\int \frac{3-2\sqrt{3}+(-3+\sqrt{3})x^4}{1-x^4+x^8}dx=\text{Exception raised: PolynomialError}$$ 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. $$\int \frac{1}{(d+e{x}^n)(a+b{x}^n+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{1}{{(d+e{x}^n)}^2(a+b{x}^n+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{1}{{(d+e{x}^n)}^3(a+b{x}^n+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{x^4}{(d+e{x}^n)(a+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{x^2}{(d+e{x}^n)(a+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{1}{(d+e{x}^n)(a+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{1}{x^2(d+e{x}^n)(a+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{x^4}{{(d+e{x}^n)}^2(a+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{x^2}{{(d+e{x}^n)}^2(a+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{1}{{(d+e{x}^n)}^2(a+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{x^{2n}}{(d+e{x}^n)(a+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{x^n}{(d+e{x}^n)(a+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{1}{(d+e{x}^n)(a+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{x^{3n}}{{(d+e{x}^n)}^2(a+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{x^{2n}}{{(d+e{x}^n)}^2(a+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{x^n}{{(d+e{x}^n)}^2(a+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{1}{{(d+e{x}^n)}^2(a+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{x^2{(d+e{x}^n)}^q}{a+c{x}^{2n}}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{x{(d+e{x}^n)}^q}{a+c{x}^{2n}}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{{(d+e{x}^n)}^q}{a+c{x}^{2n}}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{(fx{)}^m{(d+e{x}^n)}^q}{a+c{x}^{2n}}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{x^2{(d+e{x}^n)}^2}{a+b{x}^n+c{x}^{2n}}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{x^4}{(d+e{x}^n)(a+b{x}^n+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{x^2}{(d+e{x}^n)(a+b{x}^n+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{1}{(d+e{x}^n)(a+b{x}^n+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{1}{x^2(d+e{x}^n)(a+b{x}^n+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{1}{x^4(d+e{x}^n)(a+b{x}^n+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{x^4}{{(d+e{x}^n)}^2(a+b{x}^n+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{x^2}{{(d+e{x}^n)}^2(a+b{x}^n+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{1}{{(d+e{x}^n)}^2(a+b{x}^n+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{1}{x^2{(d+e{x}^n)}^2(a+b{x}^n+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{x^{3n}(d+e{x}^n)}{a+b{x}^n+c{x}^{2n}}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{x^{-2n}(d+e{x}^n)}{a+b{x}^n+c{x}^{2n}}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{x^{3n}}{(d+e{x}^n)(a+b{x}^n+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{x^{2n}}{(d+e{x}^n)(a+b{x}^n+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{x^n}{(d+e{x}^n)(a+b{x}^n+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{1}{(d+e{x}^n)(a+b{x}^n+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{x^{-n}}{(d+e{x}^n)(a+b{x}^n+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{x^{-2n}}{(d+e{x}^n)(a+b{x}^n+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{x^{-3n}}{(d+e{x}^n)(a+b{x}^n+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{x^{3n}}{{(d+e{x}^n)}^2(a+b{x}^n+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{x^{2n}}{{(d+e{x}^n)}^2(a+b{x}^n+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{x^n}{{(d+e{x}^n)}^2(a+b{x}^n+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{1}{{(d+e{x}^n)}^2(a+b{x}^n+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{x^{-3n}}{{(d+e{x}^n)}^2(a+b{x}^n+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{x^2{(d+e{x}^n)}^q}{a+b{x}^n+c{x}^{2n}}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{x{(d+e{x}^n)}^q}{a+b{x}^n+c{x}^{2n}}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{{(d+e{x}^n)}^q}{x^2(a+b{x}^n+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{(fx{)}^m{(d+e{x}^n)}^q}{a+b{x}^n+c{x}^{2n}}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{A+B{x}^n+C{x}^{2n}}{(d+e{x}^n)(a+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{A+B{x}^n+C{x}^{2n}}{{(d+e{x}^n)}^2(a+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{{(d+e{x}^n)}^2(A+B{x}^n+C{x}^{2n})}{a+b{x}^n+c{x}^{2n}}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{A+B{x}^n+C{x}^{2n}}{(d+e{x}^n)(a+b{x}^n+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{A+B{x}^n+C{x}^{2n}}{{(d+e{x}^n)}^2(a+b{x}^n+c{x}^{2n})}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int {(a+x^2)}^{5/2}{(x+\sqrt{a+x^2})}^{n}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int {(a+x^2)}^{5/2}{(x-\sqrt{a+x^2})}^{n}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int {(a+\frac{2dex}{f^2}+\frac{e^2{x}^2}{f^2})}^{3/2}{(d+ex+f\sqrt{a+\frac{2dex}{f^2}+\frac{e^2{x}^2}{f^2}})}^{n}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \sqrt{a+\frac{2dex}{f^2}+\frac{e^2{x}^2}{f^2}}{(d+ex+f\sqrt{a+\frac{2dex}{f^2}+\frac{e^2{x}^2}{f^2}})}^{n}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{{(d+ex+f\sqrt{a+\frac{2dex}{f^2}+\frac{e^2{x}^2}{f^2}})}^n}{{(a+\frac{2dex}{f^2}+\frac{e^2{x}^2}{f^2})}^{3/2}}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int {(1-(1-6b{)}^{3/2}-9b+54bx-54x^2+108x^3)}^{p}dx=\text{Exception raised: AttributeError}$$ 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. $$\int \frac{be+2cex+3de{x}^2}{{(a+bx+c{x}^2+d{x}^3)}^{5/2}}dx=\text{Exception raised: RecursionError}$$ 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. $$\int \frac{{(3-2\sqrt{2}+x^2)}^2(-3+2\sqrt{2}+x^2)}{577-408\sqrt{2}-8(-41+29\sqrt{2})x^2-2(-39+28\sqrt{2})x^4-8(-1+\sqrt{2})x^6+x^8}dx=\text{Exception raised: PolynomialError}$$ 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. $$\int \frac{-3+2\sqrt{2}+x^2}{17-12\sqrt{2}+(2-4\sqrt{2})x^2+x^4}dx=\text{Exception raised: PolynomialError}$$ 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. $$\int \frac{{(-3+2\sqrt{2})}^2-x^4}{-99+70\sqrt{2}+(-39+28\sqrt{2})x^2+(-5+6\sqrt{2})x^4-x^6}dx=\text{Exception raised: PolynomialError}$$ 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. $$\int \frac{(-3+2\sqrt{2}-x^2)(-3+2\sqrt{2}+x^2)}{-99+70\sqrt{2}+(-39+28\sqrt{2})x^2+(-5+6\sqrt{2})x^4-x^6}dx=\text{Exception raised: PolynomialError}$$ 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. $$\int \frac{{(-3+2\sqrt{2})}^3-{(-3+2\sqrt{2})}^2{x}^2-(-3+2\sqrt{2})x^4+x^6}{577-408\sqrt{2}+(328-232\sqrt{2})x^2+(78-56\sqrt{2})x^4+(8-8\sqrt{2})x^6+x^8}dx=\text{Exception raised: PolynomialError}$$ 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. $$\int \frac{{(3-2\sqrt{2}+x^2)}^2(-3+2\sqrt{2}+x^2)}{577-408\sqrt{2}+(328-232\sqrt{2})x^2+(78-56\sqrt{2})x^4+(8-8\sqrt{2})x^6+x^8}dx=\text{Exception raised: PolynomialError}$$ 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. $$\int \sqrt{\frac{1}{x}}\sqrt{x}\sqrt{a+bx}dx=\text{Exception raised: RecursionError}$$ 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. $$\int x^5{(c+d{x}^2+e\sqrt{a+b{x}^2})}^{p}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int x^3{(c+d{x}^2+e\sqrt{a+b{x}^2})}^{p}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int \frac{{(c+d{x}^2+e\sqrt{a+b{x}^2})}^p}{x^3}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int F^{f(a+b{\log }^2(c(d+ex{)}^n))}(g+hx{)}^{m}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int F^{f{(a+b\log (c(d+ex{)}^n))}^2}(g+hx{)}^{m}dx=\text{Exception raised: HeuristicGCDFailed}$$ 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. $$\int 2^{2+3x}{3}^{5+7x}dx=\text{Exception raised: IndexError}$$ 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. $$\int 2^{2+3x}{3}^{5+7x}{5}^{11+13x}dx=\text{Exception raised: IndexError}$$ 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 $710$