Optimal. Leaf size=31 \[ \frac {b^5 F^a \log ^5(F) \Gamma \left (-5,-b (c+d x)^n \log (F)\right )}{d n} \]
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Rubi [A] time = 0.04, antiderivative size = 31, normalized size of antiderivative = 1.00, 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} \[ \frac {b^5 F^a \log ^5(F) \text {Gamma}\left (-5,-b \log (F) (c+d x)^n\right )}{d n} \]
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 {b^5 F^a \Gamma \left (-5,-b (c+d x)^n \log (F)\right ) \log ^5(F)}{d n}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 31, normalized size = 1.00 \[ \frac {b^5 F^a \log ^5(F) \Gamma \left (-5,-b (c+d x)^n \log (F)\right )}{d n} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.42, size = 137, normalized size = 4.42 \[ \frac {{\left (d x + c\right )}^{5 \, n} F^{a} b^{5} {\rm Ei}\left ({\left (d x + c\right )}^{n} b \log \relax (F)\right ) \log \relax (F)^{5} - {\left ({\left (d x + c\right )}^{4 \, n} b^{4} \log \relax (F)^{4} + {\left (d x + c\right )}^{3 \, n} b^{3} \log \relax (F)^{3} + 2 \, {\left (d x + c\right )}^{2 \, n} b^{2} \log \relax (F)^{2} + 6 \, {\left (d x + c\right )}^{n} b \log \relax (F) + 24\right )} e^{\left ({\left (d x + c\right )}^{n} b \log \relax (F) + a \log \relax (F)\right )}}{120 \, {\left (d x + c\right )}^{5 \, n} d n} \]
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 [B] time = 0.12, size = 213, normalized size = 6.87 \[ -\frac {b^{5} F^{a} \Ei \left (1, -b \left (d x +c \right )^{n} \ln \relax (F )\right ) \ln \relax (F )^{5}}{120 d n}-\frac {b^{4} F^{a} F^{b \left (d x +c \right )^{n}} \left (d x +c \right )^{-n} \ln \relax (F )^{4}}{120 d n}-\frac {b^{3} F^{a} F^{b \left (d x +c \right )^{n}} \left (d x +c \right )^{-2 n} \ln \relax (F )^{3}}{120 d n}-\frac {b^{2} F^{a} F^{b \left (d x +c \right )^{n}} \left (d x +c \right )^{-3 n} \ln \relax (F )^{2}}{60 d n}-\frac {b \,F^{a} F^{b \left (d x +c \right )^{n}} \left (d x +c \right )^{-4 n} \ln \relax (F )}{20 d n}-\frac {F^{a} F^{b \left (d x +c \right )^{n}} \left (d x +c \right )^{-5 n}}{5 d n} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [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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mupad [F] time = 0.00, size = -1, normalized size = -0.03 \[ \int \frac {F^{a+b\,{\left (c+d\,x\right )}^n}}{{\left (c+d\,x\right )}^{5\,n+1}} \,d x \]
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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