Optimal. Leaf size=94 \[ \frac {F^{a+b (c+d x)^n} \left (b^4 \log ^4(F) (c+d x)^{4 n}-4 b^3 \log ^3(F) (c+d x)^{3 n}+12 b^2 \log ^2(F) (c+d x)^{2 n}-24 b \log (F) (c+d x)^n+24\right )}{b^5 d n \log ^5(F)} \]
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Rubi [C] time = 0.04, antiderivative size = 31, normalized size of antiderivative = 0.33, number of steps used = 1, number of rules used = 1, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.040, Rules used = {2218} \[ \frac {F^a \text {Gamma}\left (5,-b \log (F) (c+d x)^n\right )}{b^5 d n \log ^5(F)} \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin {align*} \int F^{a+b (c+d x)^n} (c+d x)^{-1+5 n} \, dx &=\frac {F^a \Gamma \left (5,-b (c+d x)^n \log (F)\right )}{b^5 d n \log ^5(F)}\\ \end {align*}
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Mathematica [C] time = 0.01, size = 31, normalized size = 0.33 \[ \frac {F^a \Gamma \left (5,-b (c+d x)^n \log (F)\right )}{b^5 d n \log ^5(F)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 98, normalized size = 1.04 \[ \frac {{\left ({\left (d x + c\right )}^{4 \, n} b^{4} \log \relax (F)^{4} - 4 \, {\left (d x + c\right )}^{3 \, n} b^{3} \log \relax (F)^{3} + 12 \, {\left (d x + c\right )}^{2 \, n} b^{2} \log \relax (F)^{2} - 24 \, {\left (d x + c\right )}^{n} b \log \relax (F) + 24\right )} e^{\left ({\left (d x + c\right )}^{n} b \log \relax (F) + a \log \relax (F)\right )}}{b^{5} d n \log \relax (F)^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (d x + c\right )}^{5 \, n - 1} F^{{\left (d x + c\right )}^{n} b + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 95, normalized size = 1.01 \[ \frac {\left (b^{4} \left (d x +c \right )^{4 n} \ln \relax (F )^{4}-4 b^{3} \left (d x +c \right )^{3 n} \ln \relax (F )^{3}+12 b^{2} \left (d x +c \right )^{2 n} \ln \relax (F )^{2}-24 b \left (d x +c \right )^{n} \ln \relax (F )+24\right ) F^{b \left (d x +c \right )^{n}+a}}{b^{5} d n \ln \relax (F )^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.02, size = 108, normalized size = 1.15 \[ \frac {{\left ({\left (d x + c\right )}^{4 \, n} F^{a} b^{4} \log \relax (F)^{4} - 4 \, {\left (d x + c\right )}^{3 \, n} F^{a} b^{3} \log \relax (F)^{3} + 12 \, {\left (d x + c\right )}^{2 \, n} F^{a} b^{2} \log \relax (F)^{2} - 24 \, {\left (d x + c\right )}^{n} F^{a} b \log \relax (F) + 24 \, F^{a}\right )} F^{{\left (d x + c\right )}^{n} b}}{b^{5} d n \log \relax (F)^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.01 \[ \int F^{a+b\,{\left (c+d\,x\right )}^n}\,{\left (c+d\,x\right )}^{5\,n-1} \,d x \]
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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