Optimal. Leaf size=29 \[ \text {Int}\left (\frac {1}{(c+d x)^2 \left (a+b \left (F^{e g+f g x}\right )^n\right )^3},x\right ) \]
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Rubi [A] time = 0.12, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {1}{\left (a+b \left (F^{g (e+f x)}\right )^n\right )^3 (c+d x)^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {1}{\left (a+b \left (F^{g (e+f x)}\right )^n\right )^3 (c+d x)^2} \, dx &=\int \frac {1}{\left (a+b \left (F^{e g+f g x}\right )^n\right )^3 (c+d x)^2} \, dx\\ \end {align*}
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Mathematica [A] time = 1.49, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (a+b \left (F^{g (e+f x)}\right )^n\right )^3 (c+d x)^2} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.43, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{a^{3} d^{2} x^{2} + 2 \, a^{3} c d x + a^{3} c^{2} + {\left (b^{3} d^{2} x^{2} + 2 \, b^{3} c d x + b^{3} c^{2}\right )} {\left (F^{f g x + e g}\right )}^{3 \, n} + 3 \, {\left (a b^{2} d^{2} x^{2} + 2 \, a b^{2} c d x + a b^{2} c^{2}\right )} {\left (F^{f g x + e g}\right )}^{2 \, n} + 3 \, {\left (a^{2} b d^{2} x^{2} + 2 \, a^{2} b c d x + a^{2} b c^{2}\right )} {\left (F^{f g x + e g}\right )}^{n}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left ({\left (F^{{\left (f x + e\right )} g}\right )}^{n} b + a\right )}^{3} {\left (d x + c\right )}^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.71, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (b \left (F^{\left (f x +e \right ) g}\right )^{n}+a \right )^{3} \left (d x +c \right )^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \frac {3 \, a d f g n x \log \relax (F) + 3 \, a c f g n \log \relax (F) + 2 \, {\left ({\left (F^{e g}\right )}^{n} b d f g n x \log \relax (F) + {\left (F^{e g}\right )}^{n} b c f g n \log \relax (F) + {\left (F^{e g}\right )}^{n} b d\right )} {\left (F^{f g x}\right )}^{n} + 2 \, a d}{2 \, {\left (a^{4} d^{3} f^{2} g^{2} n^{2} x^{3} \log \relax (F)^{2} + 3 \, a^{4} c d^{2} f^{2} g^{2} n^{2} x^{2} \log \relax (F)^{2} + 3 \, a^{4} c^{2} d f^{2} g^{2} n^{2} x \log \relax (F)^{2} + a^{4} c^{3} f^{2} g^{2} n^{2} \log \relax (F)^{2} + {\left ({\left (F^{e g}\right )}^{2 \, n} a^{2} b^{2} d^{3} f^{2} g^{2} n^{2} x^{3} \log \relax (F)^{2} + 3 \, {\left (F^{e g}\right )}^{2 \, n} a^{2} b^{2} c d^{2} f^{2} g^{2} n^{2} x^{2} \log \relax (F)^{2} + 3 \, {\left (F^{e g}\right )}^{2 \, n} a^{2} b^{2} c^{2} d f^{2} g^{2} n^{2} x \log \relax (F)^{2} + {\left (F^{e g}\right )}^{2 \, n} a^{2} b^{2} c^{3} f^{2} g^{2} n^{2} \log \relax (F)^{2}\right )} {\left (F^{f g x}\right )}^{2 \, n} + 2 \, {\left ({\left (F^{e g}\right )}^{n} a^{3} b d^{3} f^{2} g^{2} n^{2} x^{3} \log \relax (F)^{2} + 3 \, {\left (F^{e g}\right )}^{n} a^{3} b c d^{2} f^{2} g^{2} n^{2} x^{2} \log \relax (F)^{2} + 3 \, {\left (F^{e g}\right )}^{n} a^{3} b c^{2} d f^{2} g^{2} n^{2} x \log \relax (F)^{2} + {\left (F^{e g}\right )}^{n} a^{3} b c^{3} f^{2} g^{2} n^{2} \log \relax (F)^{2}\right )} {\left (F^{f g x}\right )}^{n}\right )}} + \int \frac {d^{2} f^{2} g^{2} n^{2} x^{2} \log \relax (F)^{2} + c^{2} f^{2} g^{2} n^{2} \log \relax (F)^{2} + 3 \, c d f g n \log \relax (F) + 3 \, d^{2} + {\left (2 \, c d f^{2} g^{2} n^{2} \log \relax (F)^{2} + 3 \, d^{2} f g n \log \relax (F)\right )} x}{a^{3} d^{4} f^{2} g^{2} n^{2} x^{4} \log \relax (F)^{2} + 4 \, a^{3} c d^{3} f^{2} g^{2} n^{2} x^{3} \log \relax (F)^{2} + 6 \, a^{3} c^{2} d^{2} f^{2} g^{2} n^{2} x^{2} \log \relax (F)^{2} + 4 \, a^{3} c^{3} d f^{2} g^{2} n^{2} x \log \relax (F)^{2} + a^{3} c^{4} f^{2} g^{2} n^{2} \log \relax (F)^{2} + {\left ({\left (F^{e g}\right )}^{n} a^{2} b d^{4} f^{2} g^{2} n^{2} x^{4} \log \relax (F)^{2} + 4 \, {\left (F^{e g}\right )}^{n} a^{2} b c d^{3} f^{2} g^{2} n^{2} x^{3} \log \relax (F)^{2} + 6 \, {\left (F^{e g}\right )}^{n} a^{2} b c^{2} d^{2} f^{2} g^{2} n^{2} x^{2} \log \relax (F)^{2} + 4 \, {\left (F^{e g}\right )}^{n} a^{2} b c^{3} d f^{2} g^{2} n^{2} x \log \relax (F)^{2} + {\left (F^{e g}\right )}^{n} a^{2} b c^{4} f^{2} g^{2} n^{2} \log \relax (F)^{2}\right )} {\left (F^{f g x}\right )}^{n}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.03 \[ \int \frac {1}{{\left (a+b\,{\left (F^{g\,\left (e+f\,x\right )}\right )}^n\right )}^3\,{\left (c+d\,x\right )}^2} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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