Integrals 101 to 200

2.4.2 Integrals 101 to 200

2.4.2.1 Sympy [F(-2)]

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

[In]

integrate((b*x+a)**m*(d*x+c)**(-3-m)*(f*x+e)*(h*x+g),x)

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.1_Linear/1.1.1.4-a+b_x-^m-c+d_x-^n-e+f_x-^p-g+h_x-^q.txt

Test ﬁle number \(15\)

Integral number in ﬁle \(129\)

2.4.2.2 Sympy [F(-2)]

Exception generated. \[ \int (a+b x)^m (c+d x)^{-4-m} (e+f x) (g+h x) \, dx=\text {Exception raised: HeuristicGCDFailed} \]

[In]

integrate((b*x+a)**m*(d*x+c)**(-4-m)*(f*x+e)*(h*x+g),x)

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.1_Linear/1.1.1.4-a+b_x-^m-c+d_x-^n-e+f_x-^p-g+h_x-^q.txt

Test ﬁle number \(15\)

Integral number in ﬁle \(130\)

2.4.2.3 Sympy [F(-2)]

Exception generated. \[ \int (a+b x)^m (c+d x)^{-5-m} (e+f x) (g+h x) \, dx=\text {Exception raised: HeuristicGCDFailed} \]

[In]

integrate((b*x+a)**m*(d*x+c)**(-5-m)*(f*x+e)*(h*x+g),x)

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.1_Linear/1.1.1.4-a+b_x-^m-c+d_x-^n-e+f_x-^p-g+h_x-^q.txt

Test ﬁle number \(15\)

Integral number in ﬁle \(131\)

2.4.2.4 Sympy [F(-2)]

Exception generated. \[ \int (a+b x)^2 (c+d x)^{-4-m} (e+f x)^m (g+h x) \, dx=\text {Exception raised: HeuristicGCDFailed} \]

[In]

integrate((b*x+a)**2*(d*x+c)**(-4-m)*(f*x+e)**m*(h*x+g),x)

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.1_Linear/1.1.1.4-a+b_x-^m-c+d_x-^n-e+f_x-^p-g+h_x-^q.txt

Test ﬁle number \(15\)

Integral number in ﬁle \(133\)

2.4.2.5 Sympy [F(-2)]

Exception generated. \[ \int (a+b x) (c+d x)^{-4-m} (e+f x)^m (g+h x) \, dx=\text {Exception raised: HeuristicGCDFailed} \]

[In]

integrate((b*x+a)*(d*x+c)**(-4-m)*(f*x+e)**m*(h*x+g),x)

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.1_Linear/1.1.1.4-a+b_x-^m-c+d_x-^n-e+f_x-^p-g+h_x-^q.txt

Test ﬁle number \(15\)

Integral number in ﬁle \(134\)

2.4.2.6 Sympy [F(-2)]

Exception generated. \[ \int (c+d x)^{-4-m} (e+f x)^m (g+h x) \, dx=\text {Exception raised: HeuristicGCDFailed} \]

[In]

integrate((d*x+c)**(-4-m)*(f*x+e)**m*(h*x+g),x)

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.1_Linear/1.1.1.4-a+b_x-^m-c+d_x-^n-e+f_x-^p-g+h_x-^q.txt

Test ﬁle number \(15\)

Integral number in ﬁle \(135\)

2.4.2.7 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.1_Linear/1.1.1.4-a+b_x-^m-c+d_x-^n-e+f_x-^p-g+h_x-^q.txt

Test ﬁle number \(15\)

Integral number in ﬁle \(137\)

2.4.2.8 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.1_Linear/1.1.1.4-a+b_x-^m-c+d_x-^n-e+f_x-^p-g+h_x-^q.txt

Test ﬁle number \(15\)

Integral number in ﬁle \(138\)

2.4.2.9 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.1_Linear/1.1.1.5_P-x-a+b_x-^m-c+d_x-^n.txt

Test ﬁle number \(16\)

Integral number in ﬁle \(30\)

2.4.2.10 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.1_Linear/1.1.1.5_P-x-a+b_x-^m-c+d_x-^n.txt

Test ﬁle number \(16\)

Integral number in ﬁle \(32\)

2.4.2.11 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.1_Linear/1.1.1.5_P-x-a+b_x-^m-c+d_x-^n.txt

Test ﬁle number \(16\)

Integral number in ﬁle \(33\)

2.4.2.12 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.1_Linear/1.1.1.5_P-x-a+b_x-^m-c+d_x-^n.txt

Test ﬁle number \(16\)

Integral number in ﬁle \(34\)

2.4.2.13 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.3-a+b_x^n-^p-c+d_x^n-^q.txt

Test ﬁle number \(26\)

Integral number in ﬁle \(303\)

2.4.2.14 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.3-a+b_x^n-^p-c+d_x^n-^q.txt

Test ﬁle number \(26\)

Integral number in ﬁle \(304\)

2.4.2.15 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.3-a+b_x^n-^p-c+d_x^n-^q.txt

Test ﬁle number \(26\)

Integral number in ﬁle \(309\)

2.4.2.16 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.3-a+b_x^n-^p-c+d_x^n-^q.txt

Test ﬁle number \(26\)

Integral number in ﬁle \(310\)

2.4.2.17 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.3-a+b_x^n-^p-c+d_x^n-^q.txt

Test ﬁle number \(26\)

Integral number in ﬁle \(312\)

2.4.2.18 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.3-a+b_x^n-^p-c+d_x^n-^q.txt

Test ﬁle number \(26\)

Integral number in ﬁle \(317\)

2.4.2.19 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.3-a+b_x^n-^p-c+d_x^n-^q.txt

Test ﬁle number \(26\)

Integral number in ﬁle \(318\)

2.4.2.20 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.3-a+b_x^n-^p-c+d_x^n-^q.txt

Test ﬁle number \(26\)

Integral number in ﬁle \(320\)

2.4.2.21 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.3-a+b_x^n-^p-c+d_x^n-^q.txt

Test ﬁle number \(26\)

Integral number in ﬁle \(325\)

2.4.2.22 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.3-a+b_x^n-^p-c+d_x^n-^q.txt

Test ﬁle number \(26\)

Integral number in ﬁle \(326\)

2.4.2.23 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.3-a+b_x^n-^p-c+d_x^n-^q.txt

Test ﬁle number \(26\)

Integral number in ﬁle \(327\)

2.4.2.24 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.3-a+b_x^n-^p-c+d_x^n-^q.txt

Test ﬁle number \(26\)

Integral number in ﬁle \(328\)

2.4.2.25 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.3-a+b_x^n-^p-c+d_x^n-^q.txt

Test ﬁle number \(26\)

Integral number in ﬁle \(333\)

2.4.2.26 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.3-a+b_x^n-^p-c+d_x^n-^q.txt

Test ﬁle number \(26\)

Integral number in ﬁle \(334\)

2.4.2.27 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.3-a+b_x^n-^p-c+d_x^n-^q.txt

Test ﬁle number \(26\)

Integral number in ﬁle \(335\)

2.4.2.28 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.3-a+b_x^n-^p-c+d_x^n-^q.txt

Test ﬁle number \(26\)

Integral number in ﬁle \(336\)

2.4.2.29 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: MellinTransformStripError >> Pole inside critical strip?

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.3-a+b_x^n-^p-c+d_x^n-^q.txt

Test ﬁle number \(26\)

Integral number in ﬁle \(347\)

2.4.2.30 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.3-a+b_x^n-^p-c+d_x^n-^q.txt

Test ﬁle number \(26\)

Integral number in ﬁle \(384\)

2.4.2.31 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.4-e_x-^m-a+b_x^n-^p-c+d_x^n-^q.txt

Test ﬁle number \(27\)

Integral number in ﬁle \(1031\)

2.4.2.32 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.4-e_x-^m-a+b_x^n-^p-c+d_x^n-^q.txt

Test ﬁle number \(27\)

Integral number in ﬁle \(1032\)

2.4.2.33 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.4-e_x-^m-a+b_x^n-^p-c+d_x^n-^q.txt

Test ﬁle number \(27\)

Integral number in ﬁle \(1033\)

2.4.2.34 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.4-e_x-^m-a+b_x^n-^p-c+d_x^n-^q.txt

Test ﬁle number \(27\)

Integral number in ﬁle \(1034\)

2.4.2.35 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.4-e_x-^m-a+b_x^n-^p-c+d_x^n-^q.txt

Test ﬁle number \(27\)

Integral number in ﬁle \(1035\)

2.4.2.36 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.4-e_x-^m-a+b_x^n-^p-c+d_x^n-^q.txt

Test ﬁle number \(27\)

Integral number in ﬁle \(1036\)

2.4.2.37 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.4-e_x-^m-a+b_x^n-^p-c+d_x^n-^q.txt

Test ﬁle number \(27\)

Integral number in ﬁle \(1037\)

2.4.2.38 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.4-e_x-^m-a+b_x^n-^p-c+d_x^n-^q.txt

Test ﬁle number \(27\)

Integral number in ﬁle \(1038\)

2.4.2.39 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: NotImplementedError >> no valid subset found

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.4-e_x-^m-a+b_x^n-^p-c+d_x^n-^q.txt

Test ﬁle number \(27\)

Integral number in ﬁle \(1042\)

2.4.2.40 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.4-e_x-^m-a+b_x^n-^p-c+d_x^n-^q.txt

Test ﬁle number \(27\)

Integral number in ﬁle \(1043\)

2.4.2.41 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.4-e_x-^m-a+b_x^n-^p-c+d_x^n-^q.txt

Test ﬁle number \(27\)

Integral number in ﬁle \(1044\)

2.4.2.42 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.4-e_x-^m-a+b_x^n-^p-c+d_x^n-^q.txt

Test ﬁle number \(27\)

Integral number in ﬁle \(1048\)

2.4.2.43 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.4-e_x-^m-a+b_x^n-^p-c+d_x^n-^q.txt

Test ﬁle number \(27\)

Integral number in ﬁle \(1049\)

2.4.2.44 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.4-e_x-^m-a+b_x^n-^p-c+d_x^n-^q.txt

Test ﬁle number \(27\)

Integral number in ﬁle \(1050\)

2.4.2.45 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.6-g_x-^m-a+b_x^n-^p-c+d_x^n-^q-e+f_x^n-^r.txt

Test ﬁle number \(28\)

Integral number in ﬁle \(26\)

2.4.2.46 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.6-g_x-^m-a+b_x^n-^p-c+d_x^n-^q-e+f_x^n-^r.txt

Test ﬁle number \(28\)

Integral number in ﬁle \(27\)

2.4.2.47 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.6-g_x-^m-a+b_x^n-^p-c+d_x^n-^q-e+f_x^n-^r.txt

Test ﬁle number \(28\)

Integral number in ﬁle \(28\)

2.4.2.48 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.6-g_x-^m-a+b_x^n-^p-c+d_x^n-^q-e+f_x^n-^r.txt

Test ﬁle number \(28\)

Integral number in ﬁle \(33\)

2.4.2.49 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.6-g_x-^m-a+b_x^n-^p-c+d_x^n-^q-e+f_x^n-^r.txt

Test ﬁle number \(28\)

Integral number in ﬁle \(34\)

2.4.2.50 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.6-g_x-^m-a+b_x^n-^p-c+d_x^n-^q-e+f_x^n-^r.txt

Test ﬁle number \(28\)

Integral number in ﬁle \(39\)

2.4.2.51 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.6-g_x-^m-a+b_x^n-^p-c+d_x^n-^q-e+f_x^n-^r.txt

Test ﬁle number \(28\)

Integral number in ﬁle \(41\)

2.4.2.52 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.6-g_x-^m-a+b_x^n-^p-c+d_x^n-^q-e+f_x^n-^r.txt

Test ﬁle number \(28\)

Integral number in ﬁle \(43\)

2.4.2.53 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.6-g_x-^m-a+b_x^n-^p-c+d_x^n-^q-e+f_x^n-^r.txt

Test ﬁle number \(28\)

Integral number in ﬁle \(44\)

2.4.2.54 Sympy [F(-2)]

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

[In]

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)

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.8_P-x-c_x-^m-a+b_x^n-^p.txt

Test ﬁle number \(29\)

Integral number in ﬁle \(592\)

2.4.2.55 Sympy [F(-2)]

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

[In]

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)

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.8_P-x-c_x-^m-a+b_x^n-^p.txt

Test ﬁle number \(29\)

Integral number in ﬁle \(593\)

2.4.2.56 Sympy [F(-2)]

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

[In]

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)

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.3_General/1.1.3.8_P-x-c_x-^m-a+b_x^n-^p.txt

Test ﬁle number \(29\)

Integral number in ﬁle \(594\)

2.4.2.57 Sympy [F(-2)]

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

[In]

integrate(1/(b*x**(1-2*m)+a*x**m)**3,x)

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.1_Binomial_products/1.1.4_Improper/1.1.4.2-c_x-^m-a_x^j+b_x^n-^p.txt

Test ﬁle number \(30\)

Integral number in ﬁle \(337\)

2.4.2.58 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: TypeError >> Invalid NaN comparison

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.2-d+e_x-^m-a+b_x+c_x^2-^p.txt

Test ﬁle number \(33\)

Integral number in ﬁle \(1099\)

2.4.2.59 Sympy [F(-2)]

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

[In]

integrate((b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**12,x)

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.2-d+e_x-^m-a+b_x+c_x^2-^p.txt

Test ﬁle number \(33\)

Integral number in ﬁle \(1586\)

2.4.2.60 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.2-d+e_x-^m-a+b_x+c_x^2-^p.txt

Test ﬁle number \(33\)

Integral number in ﬁle \(1737\)

2.4.2.61 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.2-d+e_x-^m-a+b_x+c_x^2-^p.txt

Test ﬁle number \(33\)

Integral number in ﬁle \(1741\)

2.4.2.62 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.2-d+e_x-^m-a+b_x+c_x^2-^p.txt

Test ﬁle number \(33\)

Integral number in ﬁle \(1742\)

2.4.2.63 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.2-d+e_x-^m-a+b_x+c_x^2-^p.txt

Test ﬁle number \(33\)

Integral number in ﬁle \(1743\)

2.4.2.64 Sympy [F(-2)]

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

[In]

integrate((e*x+d)**m*(b**2*x**2+2*a*b*x+a**2)**(5+p),x)

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.2-d+e_x-^m-a+b_x+c_x^2-^p.txt

Test ﬁle number \(33\)

Integral number in ﬁle \(1756\)

2.4.2.65 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.2-d+e_x-^m-a+b_x+c_x^2-^p.txt

Test ﬁle number \(33\)

Integral number in ﬁle \(2090\)

2.4.2.66 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: TypeError >> Invalid NaN comparison

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.2-d+e_x-^m-a+b_x+c_x^2-^p.txt

Test ﬁle number \(33\)

Integral number in ﬁle \(2105\)

2.4.2.67 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.2-d+e_x-^m-a+b_x+c_x^2-^p.txt

Test ﬁle number \(33\)

Integral number in ﬁle \(2555\)

2.4.2.68 Sympy [F(-2)]

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

[In]

integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**12,x)

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.3-d+e_x-^m-f+g_x-a+b_x+c_x^2-^p.txt

Test ﬁle number \(34\)

Integral number in ﬁle \(1756\)

2.4.2.69 Sympy [F(-2)]

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

[In]

integrate((B*x+A)*(e*x+d)**m*(b**2*x**2+2*a*b*x+a**2)**(5/2),x)

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.3-d+e_x-^m-f+g_x-a+b_x+c_x^2-^p.txt

Test ﬁle number \(34\)

Integral number in ﬁle \(1888\)

2.4.2.70 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.3-d+e_x-^m-f+g_x-a+b_x+c_x^2-^p.txt

Test ﬁle number \(34\)

Integral number in ﬁle \(1892\)

2.4.2.71 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.3-d+e_x-^m-f+g_x-a+b_x+c_x^2-^p.txt

Test ﬁle number \(34\)

Integral number in ﬁle \(1893\)

2.4.2.72 Sympy [F(-2)]

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

[In]

integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**12,x)

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.3-d+e_x-^m-f+g_x-a+b_x+c_x^2-^p.txt

Test ﬁle number \(34\)

Integral number in ﬁle \(2009\)

2.4.2.73 Sympy [F(-2)]

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

[In]

integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**13,x)

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.3-d+e_x-^m-f+g_x-a+b_x+c_x^2-^p.txt

Test ﬁle number \(34\)

Integral number in ﬁle \(2010\)

2.4.2.74 Sympy [F(-2)]

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

[In]

integrate((b*x+a)*(b**2*x**2+2*a*b*x+a**2)**(5/2)/(e*x+d)**17,x)

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.3-d+e_x-^m-f+g_x-a+b_x+c_x^2-^p.txt

Test ﬁle number \(34\)

Integral number in ﬁle \(2014\)

2.4.2.75 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.3-d+e_x-^m-f+g_x-a+b_x+c_x^2-^p.txt

Test ﬁle number \(34\)

Integral number in ﬁle \(2151\)

2.4.2.76 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.3-d+e_x-^m-f+g_x-a+b_x+c_x^2-^p.txt

Test ﬁle number \(34\)

Integral number in ﬁle \(2155\)

2.4.2.77 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.3-d+e_x-^m-f+g_x-a+b_x+c_x^2-^p.txt

Test ﬁle number \(34\)

Integral number in ﬁle \(2156\)

2.4.2.78 Sympy [F(-2)]

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

[In]

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)

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.3-d+e_x-^m-f+g_x-a+b_x+c_x^2-^p.txt

Test ﬁle number \(34\)

Integral number in ﬁle \(2285\)

2.4.2.79 Sympy [F(-2)]

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

[In]

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)

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.3-d+e_x-^m-f+g_x-a+b_x+c_x^2-^p.txt

Test ﬁle number \(34\)

Integral number in ﬁle \(2290\)

2.4.2.80 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.4-d+e_x-^m-f+g_x-^n-a+b_x+c_x^2-^p.txt

Test ﬁle number \(35\)

Integral number in ﬁle \(232\)

2.4.2.81 Sympy [F(-2)]

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

[In]

integrate((g*x)**m/(e*x+d)**2/(-e**2*x**2+d**2)**(7/2),x)

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.4-d+e_x-^m-f+g_x-^n-a+b_x+c_x^2-^p.txt

Test ﬁle number \(35\)

Integral number in ﬁle \(238\)

2.4.2.82 Sympy [F(-2)]

Exception generated. \[ \int \frac {(g x)^m}{(d+e x)^3 \left (d^2-e^2 x^2\right )^{7/2}} \, dx=\text {Exception raised: HeuristicGCDFailed} \]

[In]

integrate((g*x)**m/(e*x+d)**3/(-e**2*x**2+d**2)**(7/2),x)

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.4-d+e_x-^m-f+g_x-^n-a+b_x+c_x^2-^p.txt

Test ﬁle number \(35\)

Integral number in ﬁle \(239\)

2.4.2.83 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.4-d+e_x-^m-f+g_x-^n-a+b_x+c_x^2-^p.txt

Test ﬁle number \(35\)

Integral number in ﬁle \(542\)

2.4.2.84 Sympy [F(-2)]

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

[In]

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)

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.4-d+e_x-^m-f+g_x-^n-a+b_x+c_x^2-^p.txt

Test ﬁle number \(35\)

Integral number in ﬁle \(767\)

2.4.2.85 Sympy [F(-2)]

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

[In]

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)

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.4-d+e_x-^m-f+g_x-^n-a+b_x+c_x^2-^p.txt

Test ﬁle number \(35\)

Integral number in ﬁle \(772\)

2.4.2.86 Sympy [F(-2)]

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

[In]

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)

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.4-d+e_x-^m-f+g_x-^n-a+b_x+c_x^2-^p.txt

Test ﬁle number \(35\)

Integral number in ﬁle \(774\)

2.4.2.87 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.4-d+e_x-^m-f+g_x-^n-a+b_x+c_x^2-^p.txt

Test ﬁle number \(35\)

Integral number in ﬁle \(810\)

2.4.2.88 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.4-d+e_x-^m-f+g_x-^n-a+b_x+c_x^2-^p.txt

Test ﬁle number \(35\)

Integral number in ﬁle \(813\)

2.4.2.89 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.4-d+e_x-^m-f+g_x-^n-a+b_x+c_x^2-^p.txt

Test ﬁle number \(35\)

Integral number in ﬁle \(923\)

2.4.2.90 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.4-d+e_x-^m-f+g_x-^n-a+b_x+c_x^2-^p.txt

Test ﬁle number \(35\)

Integral number in ﬁle \(928\)

2.4.2.91 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.4-d+e_x-^m-f+g_x-^n-a+b_x+c_x^2-^p.txt

Test ﬁle number \(35\)

Integral number in ﬁle \(944\)

2.4.2.92 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.4-d+e_x-^m-f+g_x-^n-a+b_x+c_x^2-^p.txt

Test ﬁle number \(35\)

Integral number in ﬁle \(953\)

2.4.2.93 Sympy [F(-2)]

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

[In]

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

)

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.1_Quadratic/1.2.1.9_P-x-d+e_x-^m-a+b_x+c_x^2-^p.txt

Test ﬁle number \(38\)

Integral number in ﬁle \(139\)

2.4.2.94 Sympy [F(-2)]

Exception generated. \[ \int \frac {\sqrt {2}-x^2}{1-\sqrt {2} x^2+x^4} \, dx=\text {Exception raised: PolynomialError} \]

[In]

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

[Out]

Exception raised: PolynomialError >> 1/(128*_t**4 - 16*sqrt(2)*_t**2 + 1) contains an element of the set of ge

nerators.

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.2_Quartic/1.2.2.3-d+e_x^2-^m-a+b_x^2+c_x^4-^p.txt

Test ﬁle number \(40\)

Integral number in ﬁle \(102\)

2.4.2.95 Sympy [F(-2)]

Exception generated. \[ \int \frac {\sqrt {2}+x^2}{1+\sqrt {2} x^2+x^4} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate((x**2+2**(1/2))/(1+x**4+x**2*2**(1/2)),x)

[Out]

Exception raised: PolynomialError >> 1/(128*_t**4 + 16*sqrt(2)*_t**2 + 1) contains an element of the set of ge

nerators.

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.2_Quartic/1.2.2.3-d+e_x^2-^m-a+b_x^2+c_x^4-^p.txt

Test ﬁle number \(40\)

Integral number in ﬁle \(103\)

2.4.2.96 Sympy [F(-2)]

Exception generated. \[ \int \frac {2 \sqrt {a}-x^2}{a-\sqrt {a} x^2+x^4} \, dx=\text {Exception raised: PolynomialError} \]

[In]

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

[Out]

Exception raised: PolynomialError >> 1/(64*_t**4*a - 16*_t**2*sqrt(a) + 1) contains an element of the set of g

enerators.

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.2_Quartic/1.2.2.3-d+e_x^2-^m-a+b_x^2+c_x^4-^p.txt

Test ﬁle number \(40\)

Integral number in ﬁle \(107\)

2.4.2.97 Sympy [F(-2)]

Exception generated. \[ \int \frac {A+B x^2}{a-\sqrt {a} x^2+x^4} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate((B*x**2+A)/(a+x**4-x**2*a**(1/2)),x)

[Out]

Exception raised: PolynomialError >> 1/(64*_t**4*a - 16*_t**2*B**2*sqrt(a) + B**4) contains an element of the

set of generators.

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.2_Quartic/1.2.2.3-d+e_x^2-^m-a+b_x^2+c_x^4-^p.txt

Test ﬁle number \(40\)

Integral number in ﬁle \(110\)

2.4.2.98 Sympy [F(-2)]

Exception generated. \[ \int \frac {A+B x^2}{a-\sqrt {a c} x^2+c x^4} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate((B*x**2+A)/(a+c*x**4-x**2*(a*c)**(1/2)),x)

[Out]

Exception raised: PolynomialError >> 1/(64*_t**4*a*c**3 - 16*_t**2*B**2*c*sqrt(a*c) + B**4) contains an elemen

t of the set of generators.

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.2_Quartic/1.2.2.3-d+e_x^2-^m-a+b_x^2+c_x^4-^p.txt

Test ﬁle number \(40\)

Integral number in ﬁle \(111\)

2.4.2.99 Sympy [F(-2)]

Exception generated. \[ \int \frac {A+B x^2}{a-\sqrt {a} \sqrt {c} x^2+c x^4} \, dx=\text {Exception raised: PolynomialError} \]

[In]

integrate((B*x**2+A)/(a+c*x**4-x**2*a**(1/2)*c**(1/2)),x)

[Out]

Exception raised: PolynomialError >> 1/(64*_t**4*a*c**5 - 16*_t**2*B**2*sqrt(a)*c**(7/2) + B**4*c**2) contains

an element of the set of generators.

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.2_Quartic/1.2.2.3-d+e_x^2-^m-a+b_x^2+c_x^4-^p.txt

Test ﬁle number \(40\)

Integral number in ﬁle \(112\)

2.4.2.100 Sympy [F(-2)]

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

[In]

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

[Out]

Exception raised: HeuristicGCDFailed >> no luck

input ﬁle name 1_Algebraic_functions/1.2_Trinomial_products/1.2.3_General/1.2.3.2-d_x-^m-a+b_x^n+c_x^-2_n-^p.txt

Test ﬁle number \(46\)

Integral number in ﬁle \(498\)

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