Optimal. Leaf size=27 \[ \frac {F^{a+b (c+d x)^n}}{b d n \log (F)} \]
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Rubi [A] time = 0.04, antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {2209} \[ \frac {F^{a+b (c+d x)^n}}{b d n \log (F)} \]
Antiderivative was successfully verified.
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Rule 2209
Rubi steps
\begin {align*} \int F^{a+b (c+d x)^n} (c+d x)^{-1+n} \, dx &=\frac {F^{a+b (c+d x)^n}}{b d n \log (F)}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 27, normalized size = 1.00 \[ \frac {F^{a+b (c+d x)^n}}{b d n \log (F)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 31, normalized size = 1.15 \[ \frac {e^{\left ({\left (d x + c\right )}^{n} b \log \relax (F) + a \log \relax (F)\right )}}{b d n \log \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.30, size = 27, normalized size = 1.00 \[ \frac {F^{{\left (d x + c\right )}^{n} b + a}}{b d n \log \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 32, normalized size = 1.19 \[ \frac {{\mathrm e}^{\left (b \,{\mathrm e}^{n \ln \left (d x +c \right )}+a \right ) \ln \relax (F )}}{b d n \ln \relax (F )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.90, size = 27, normalized size = 1.00 \[ \frac {F^{{\left (d x + c\right )}^{n} b + a}}{b d n \log \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.68, size = 27, normalized size = 1.00 \[ \frac {F^{a+b\,{\left (c+d\,x\right )}^n}}{b\,d\,n\,\ln \relax (F)} \]
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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