2.4.0 Integrals 201 to 300

Integrals 201 to 300

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test ﬁle number \(56\)

Integral number in ﬁle \(550\)

Sympy [F(-2)]

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

integrate(x**(-1-n*(-3+p))*(a+b*x**n)**p/(c+d*x**n),x)

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test ﬁle number \(56\)

Integral number in ﬁle \(557\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test ﬁle number \(56\)

Integral number in ﬁle \(558\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test ﬁle number \(56\)

Integral number in ﬁle \(564\)

Sympy [F(-2)]

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

integrate(x**(-1-n*(3+2*p))*(a+b*x**n)**p*(c+d*x**n)**p,x)

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test ﬁle number \(56\)

Integral number in ﬁle \(565\)

Sympy [F(-2)]

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

integrate(x**(-1-n*(2+2*p))*(a+b*x**n)**p*(c+d*x**n)**p,x)

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test ﬁle number \(56\)

Integral number in ﬁle \(566\)

Sympy [F(-2)]

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

integrate(x**(-1-n*(1+2*p))*(a+b*x**n)**p*(c+d*x**n)**p,x)

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test ﬁle number \(56\)

Integral number in ﬁle \(567\)

Sympy [F(-2)]

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

integrate(x**(-1-n*(-1+2*p))*(a+b*x**n)**p*(c+d*x**n)**p,x)

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test ﬁle number \(56\)

Integral number in ﬁle \(569\)

Sympy [F(-2)]

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

integrate(x**(-1+3*n)*(a+b*x**n)**p*(c+d*x**n)**q,x)

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test ﬁle number \(56\)

Integral number in ﬁle \(570\)

Sympy [F(-2)]

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

integrate(x**(-1+2*n)*(a+b*x**n)**p*(c+d*x**n)**q,x)

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test ﬁle number \(56\)

Integral number in ﬁle \(571\)

Sympy [F(-2)]

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

integrate(x**(-1+n)*(a+b*x**n)**p*(c+d*x**n)**q,x)

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test ﬁle number \(56\)

Integral number in ﬁle \(572\)

Sympy [F(-2)]

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

integrate(x**(-1-n)*(a+b*x**n)**p*(c+d*x**n)**q,x)

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test ﬁle number \(56\)

Integral number in ﬁle \(574\)

Sympy [F(-2)]

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

integrate(x**(-1-2*n)*(a+b*x**n)**p*(c+d*x**n)**q,x)

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.4/56_1.1.3.4_c

Test ﬁle number \(56\)

Integral number in ﬁle \(575\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/58_1.1.3.5

Test ﬁle number \(58\)

Integral number in ﬁle \(7\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/58_1.1.3.5

Test ﬁle number \(58\)

Integral number in ﬁle \(8\)

Sympy [F(-2)]

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

integrate((a+b*x**n)**p*(c+d*x**n)**q,x)

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/58_1.1.3.5

Test ﬁle number \(58\)

Integral number in ﬁle \(9\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/58_1.1.3.5

Test ﬁle number \(58\)

Integral number in ﬁle \(10\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.6/59_1.1.3.6_a

Test ﬁle number \(59\)

Integral number in ﬁle \(38\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.6/59_1.1.3.6_a

Test ﬁle number \(59\)

Integral number in ﬁle \(44\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.6/59_1.1.3.6_a

Test ﬁle number \(59\)

Integral number in ﬁle \(45\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.6/59_1.1.3.6_a

Test ﬁle number \(59\)

Integral number in ﬁle \(46\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.6/59_1.1.3.6_a

Test ﬁle number \(59\)

Integral number in ﬁle \(47\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.6/59_1.1.3.6_a

Test ﬁle number \(59\)

Integral number in ﬁle \(51\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.6/59_1.1.3.6_a

Test ﬁle number \(59\)

Integral number in ﬁle \(52\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.6/59_1.1.3.6_a

Test ﬁle number \(59\)

Integral number in ﬁle \(57\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.6/59_1.1.3.6_a

Test ﬁle number \(59\)

Integral number in ﬁle \(60\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.6/59_1.1.3.6_a

Test ﬁle number \(59\)

Integral number in ﬁle \(61\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.6/59_1.1.3.6_a

Test ﬁle number \(59\)

Integral number in ﬁle \(62\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.6/59_1.1.3.6_a

Test ﬁle number \(59\)

Integral number in ﬁle \(63\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.6/59_1.1.3.6_a

Test ﬁle number \(59\)

Integral number in ﬁle \(64\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.6/59_1.1.3.6_a

Test ﬁle number \(59\)

Integral number in ﬁle \(65\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.6/59_1.1.3.6_a

Test ﬁle number \(59\)

Integral number in ﬁle \(66\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.6/59_1.1.3.6_a

Test ﬁle number \(59\)

Integral number in ﬁle \(85\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.6/59_1.1.3.6_a

Test ﬁle number \(59\)

Integral number in ﬁle \(86\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.6/59_1.1.3.6_a

Test ﬁle number \(59\)

Integral number in ﬁle \(87\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.6/59_1.1.3.6_a

Test ﬁle number \(59\)

Integral number in ﬁle \(88\)

Sympy [F(-2)]

Exception generated. \[ \int \left (a+b x^n\right )^p \left (A+B x^n+C x^{2 n}+D x^{3 n}\right ) \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((a+b*x**n)**p*(A+B*x**n+C*x**(2*n)+D*x**(3*n)),x)

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.7/63_1.1.3.7_c

Test ﬁle number \(63\)

Integral number in ﬁle \(70\)

Sympy [F(-2)]

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

integrate((h*x)**(-n*p-n-1)*(a+b*x**n)**p*(c+d*x**n)**p*(a*c-b*d*x**(2*n)) 
,x)

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.8/66_1.1.3.8_c

Test ﬁle number \(66\)

Integral number in ﬁle \(36\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.8/66_1.1.3.8_c

Test ﬁle number \(66\)

Integral number in ﬁle \(37\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/1.1.3.8/66_1.1.3.8_c

Test ﬁle number \(66\)

Integral number in ﬁle \(38\)

Sympy [F(-2)]

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

integrate((a+b*x**n)**p*(c+d*x**n)**q*(a*A*c+A*(b*c*(1+n*(p+1))+a*d*(1+n*( 
1+q)))*x**n+A*b*d*(1+n*(2+p+q))*x**(2*n)),x)

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/67_1.1.3.9

Test ﬁle number \(67\)

Integral number in ﬁle \(5\)

Sympy [F(-2)]

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

integrate(x**m*(C*x**3+B*x**2+A)*(a+b*x**n)**p*(c+d*x**n)**q,x)

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.3_General_binomial/68_1.1.3.10

Test ﬁle number \(68\)

Integral number in ﬁle \(6\)

Sympy [F(-2)]

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

integrate((e*x)**m*(-d**2*x**2+c**2)**(5/2)/(d*x+c)**3,x)

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.4_Linear_quadratic_binomial/72_1.2.1.4

Test ﬁle number \(72\)

Integral number in ﬁle \(1170\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.4_Linear_quadratic_binomial/73_1.2.1.5

Test ﬁle number \(73\)

Integral number in ﬁle \(1788\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.4_Linear_quadratic_binomial/73_1.2.1.5

Test ﬁle number \(73\)

Integral number in ﬁle \(1822\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.4_Linear_quadratic_binomial/73_1.2.1.5

Test ﬁle number \(73\)

Integral number in ﬁle \(1948\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.4_Linear_quadratic_binomial/75_x1_2.2_b_symbolic

Test ﬁle number \(75\)

Integral number in ﬁle \(220\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.4_Linear_quadratic_binomial/75_x1_2.2_b_symbolic

Test ﬁle number \(75\)

Integral number in ﬁle \(281\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.4_Linear_quadratic_binomial/75_x1_2.2_b_symbolic

Test ﬁle number \(75\)

Integral number in ﬁle \(371\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.1_Binomial/1.1.5_Nested_general_binomial/77_1.1.5.2

Test ﬁle number \(77\)

Integral number in ﬁle \(295\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (a^2+2 a b x+b^2 x^2\right )^{5/2}}{(d+e x)^7} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**7,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/1.2.1.2/90_1.2.1.2_b

Test ﬁle number \(90\)

Integral number in ﬁle \(303\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (a^2+2 a b x+b^2 x^2\right )^{5/2}}{(d+e x)^{12}} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**12,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/1.2.1.2/90_1.2.1.2_b

Test ﬁle number \(90\)

Integral number in ﬁle \(308\)

Sympy [F(-2)]

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

integrate((e*x+d)**m*(b**2*x**2+2*a*b*x+a**2)**(5/2),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/1.2.1.2/90_1.2.1.2_b

Test ﬁle number \(90\)

Integral number in ﬁle \(417\)

Sympy [F(-2)]

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

integrate((e*x+d)**m*((b*x+a)**2)**(1/2),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/1.2.1.2/90_1.2.1.2_b

Test ﬁle number \(90\)

Integral number in ﬁle \(419\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.1_Quadratic_trinomial/1.2.1.2/90_1.2.1.2_b

Test ﬁle number \(90\)

Integral number in ﬁle \(421\)

Sympy [F(-2)]

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

integrate((e*x+d)**m/(b**2*x**2+2*a*b*x+a**2)**(5/2),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/1.2.1.2/90_1.2.1.2_b

Test ﬁle number \(90\)

Integral number in ﬁle \(422\)

Sympy [F(-2)]

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

integrate((e*x+d)**p/((c*e**2*x**2+2*c*d*e*x+c*d**2)**p),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/1.2.1.2/90_1.2.1.2_b

Test ﬁle number \(90\)

Integral number in ﬁle \(446\)

Sympy [F(-2)]

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

integrate((e*x+d)**m*(b**2*x**2+2*a*b*x+a**2)**p,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/1.2.1.2/90_1.2.1.2_b

Test ﬁle number \(90\)

Integral number in ﬁle \(451\)

Sympy [F(-2)]

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

integrate((e*x+d)**m*(b**2*x**2+2*a*b*x+a**2)**(5+p),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/1.2.1.2/90_1.2.1.2_b

Test ﬁle number \(90\)

Integral number in ﬁle \(452\)

Sympy [F(-2)]

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

integrate((e*x+d)**m/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**4,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/1.2.1.2/91_1.2.1.2_c

Test ﬁle number \(91\)

Integral number in ﬁle \(388\)

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/1.2.1.2/91_1.2.1.2_c

Test ﬁle number \(91\)

Integral number in ﬁle \(403\)

Sympy [F(-2)]

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

integrate((e*x+d)**m*(c*x**2+b*x+a)**(5/2),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/1.2.1.2/92_1.2.1.2_d

Test ﬁle number \(92\)

Integral number in ﬁle \(767\)

Sympy [F(-2)]

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

integrate((f*x+e)**n*(-d**2*x**2+1)**(3/2)/(-d*x+1)**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/1.2.1.3/93_1.2.1.3_a

Test ﬁle number \(93\)

Integral number in ﬁle \(127\)

Sympy [F(-2)]

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

integrate((g*x+f)**n*(-e**2*x**2+d**2)**p/(e*x+d),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/1.2.1.3/93_1.2.1.3_a

Test ﬁle number \(93\)

Integral number in ﬁle \(138\)

Sympy [F(-2)]

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

integrate((e*x+d)**m*(c*x**2+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/1.2.1.3/95_1.2.1.3_c

Test ﬁle number \(95\)

Integral number in ﬁle \(153\)

Sympy [F(-2)]

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

integrate((e*x+d)**m*(c*x**2+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/1.2.1.3/95_1.2.1.3_c

Test ﬁle number \(95\)

Integral number in ﬁle \(159\)

Sympy [F(-2)]

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

integrate((e*x+d)**m*(c*x**2+a)/(f*x+e)**(3/2),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/1.2.1.3/95_1.2.1.3_c

Test ﬁle number \(95\)

Integral number in ﬁle \(161\)

Sympy [F(-2)]

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

integrate((e*x+d)**m*(g*x+f)**n*(c*x**2+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/1.2.1.3/95_1.2.1.3_c

Test ﬁle number \(95\)

Integral number in ﬁle \(172\)

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/1.2.1.3/97_1.2.1.3_d2

Test ﬁle number \(97\)

Integral number in ﬁle \(111\)

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/1.2.1.3/97_1.2.1.3_d2

Test ﬁle number \(97\)

Integral number in ﬁle \(114\)

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/1.2.1.3/97_1.2.1.3_d2

Test ﬁle number \(97\)

Integral number in ﬁle \(115\)

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/1.2.1.3/97_1.2.1.3_d2

Test ﬁle number \(97\)

Integral number in ﬁle \(116\)

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/1.2.1.3/97_1.2.1.3_d2

Test ﬁle number \(97\)

Integral number in ﬁle \(118\)

Sympy [F(-2)]

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

integrate((e*x+d)**m*(g*x+f)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2),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/1.2.1.3/97_1.2.1.3_d2

Test ﬁle number \(97\)

Integral number in ﬁle \(254\)

Sympy [F(-2)]

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

integrate((e*x+d)**m*(g*x+f)/(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(7/2),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/1.2.1.3/97_1.2.1.3_d2

Test ﬁle number \(97\)

Integral number in ﬁle \(255\)

Sympy [F(-2)]

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

integrate(x**3*(e*x+d)**m/(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/1.2.1.3/99_1.2.1.3_e2

Test ﬁle number \(99\)

Integral number in ﬁle \(125\)

Sympy [F(-2)]

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

integrate((e*x+d)**m*(c*x**2+b*x+a)**p/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/1.2.1.3/99_1.2.1.3_e2

Test ﬁle number \(99\)

Integral number in ﬁle \(138\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(a+b x) \left (a^2+2 a b x+b^2 x^2\right )^{3/2}}{(d+e x)^{12}} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**12,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/1.2.1.3/101_1.2.1.3_f1

Test ﬁle number \(101\)

Integral number in ﬁle \(146\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(a+b x) \left (a^2+2 a b x+b^2 x^2\right )^{5/2}}{(d+e x)^7} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**7,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/1.2.1.3/101_1.2.1.3_f1

Test ﬁle number \(101\)

Integral number in ﬁle \(163\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(a+b x) \left (a^2+2 a b x+b^2 x^2\right )^{5/2}}{(d+e x)^{12}} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**12,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/1.2.1.3/101_1.2.1.3_f1

Test ﬁle number \(101\)

Integral number in ﬁle \(168\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(a+b x) \left (a^2+2 a b x+b^2 x^2\right )^{5/2}}{(d+e x)^{13}} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**13,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/1.2.1.3/101_1.2.1.3_f1

Test ﬁle number \(101\)

Integral number in ﬁle \(169\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(a+b x) \left (a^2+2 a b x+b^2 x^2\right )^{5/2}}{(d+e x)^{14}} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**14,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/1.2.1.3/101_1.2.1.3_f1

Test ﬁle number \(101\)

Integral number in ﬁle \(170\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(a+b x) \left (a^2+2 a b x+b^2 x^2\right )^{5/2}}{(d+e x)^{17}} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**17,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/1.2.1.3/101_1.2.1.3_f1

Test ﬁle number \(101\)

Integral number in ﬁle \(173\)

Sympy [F(-2)]

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

integrate((b*x+a)*(e*x+d)**m*(b**2*x**2+2*a*b*x+a**2)**(5/2),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/1.2.1.3/101_1.2.1.3_f1

Test ﬁle number \(101\)

Integral number in ﬁle \(260\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.1_Quadratic_trinomial/1.2.1.3/101_1.2.1.3_f1

Test ﬁle number \(101\)

Integral number in ﬁle \(261\)

Sympy [F(-2)]

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

integrate((b*x+a)*(e*x+d)**m*((b*x+a)**2)**(1/2),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/1.2.1.3/101_1.2.1.3_f1

Test ﬁle number \(101\)

Integral number in ﬁle \(262\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.1_Quadratic_trinomial/1.2.1.3/101_1.2.1.3_f1

Test ﬁle number \(101\)

Integral number in ﬁle \(264\)

Sympy [F(-2)]

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

integrate((b*x+a)*(e*x+d)**m/(b**2*x**2+2*a*b*x+a**2)**(5/2),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/1.2.1.3/101_1.2.1.3_f1

Test ﬁle number \(101\)

Integral number in ﬁle \(265\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(A+B x) \left (a^2+2 a b x+b^2 x^2\right )^{3/2}}{(d+e x)^{12}} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(3/2)/(e*x+d)**12,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/1.2.1.3/101_1.2.1.3_f1

Test ﬁle number \(101\)

Integral number in ﬁle \(407\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(A+B x) \left (a^2+2 a b x+b^2 x^2\right )^{5/2}}{(d+e x)^7} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**7,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/1.2.1.3/101_1.2.1.3_f1

Test ﬁle number \(101\)

Integral number in ﬁle \(421\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(A+B x) \left (a^2+2 a b x+b^2 x^2\right )^{5/2}}{(d+e x)^{12}} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**12,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/1.2.1.3/101_1.2.1.3_f1

Test ﬁle number \(101\)

Integral number in ﬁle \(426\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(A+B x) \left (a^2+2 a b x+b^2 x^2\right )^{5/2}}{(d+e x)^{13}} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**13,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/1.2.1.3/101_1.2.1.3_f1

Test ﬁle number \(101\)

Integral number in ﬁle \(427\)

Sympy [F(-2)]

Exception generated. \[ \int \frac {(A+B x) \left (a^2+2 a b x+b^2 x^2\right )^{5/2}}{(d+e x)^{14}} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**14,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/1.2.1.3/101_1.2.1.3_f1

Test ﬁle number \(101\)

Integral number in ﬁle \(428\)

Sympy [F(-2)]

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

integrate((B*x+A)*(e*x+d)**m*(b**2*x**2+2*a*b*x+a**2)**(5/2),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/1.2.1.3/101_1.2.1.3_f1

Test ﬁle number \(101\)

Integral number in ﬁle \(507\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.1_Quadratic_trinomial/1.2.1.3/101_1.2.1.3_f1

Test ﬁle number \(101\)

Integral number in ﬁle \(508\)

Sympy [F(-2)]

Exception generated. \[ \int (A+B x) (d+e x)^m \sqrt {a^2+2 a b x+b^2 x^2} \, dx=\text {Exception raised: HeuristicGCDFailed} \] Input:

integrate((B*x+A)*(e*x+d)**m*((b*x+a)**2)**(1/2),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/1.2.1.3/101_1.2.1.3_f1

Test ﬁle number \(101\)

Integral number in ﬁle \(509\)

Sympy [F(-2)]

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

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

Output:

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name test_cases/rubi_tests/1_Algebraic_functions/1.2_Trinomial/1.2.1_Quadratic_trinomial/1.2.1.3/101_1.2.1.3_f1

Test ﬁle number \(101\)

Integral number in ﬁle \(511\)

Sympy [F(-2)]

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

integrate((B*x+A)*(e*x+d)**m*(b**2*x**2+2*a*b*x+a**2)**p,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/1.2.1.3/101_1.2.1.3_f1

Test ﬁle number \(101\)

Integral number in ﬁle \(512\)

Sympy [F(-2)]

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

integrate((g*x+f)*(c*x**2+b*x+a)**(7/2)/(e*x+d)**7,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/1.2.1.3/101_1.2.1.3_f1

Test ﬁle number \(101\)

Integral number in ﬁle \(908\)

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/1.2.1.3/102_1.2.1.3_f2

Test ﬁle number \(102\)

Integral number in ﬁle \(699\)

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