Optimal. Leaf size=27 \[ \frac{F^{a+b (c+d x)^n}}{b d n \log (F)} \]
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Rubi [A] time = 0.037157, antiderivative size = 27, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0072523, size = 27, normalized size = 1. \[ \frac{F^{a+b (c+d x)^n}}{b d n \log (F)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.034, size = 32, normalized size = 1.2 \begin{align*}{\frac{{{\rm e}^{ \left ( a+b{{\rm e}^{n\ln \left ( dx+c \right ) }} \right ) \ln \left ( F \right ) }}}{\ln \left ( F \right ) bdn}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.968427, size = 36, normalized size = 1.33 \begin{align*} \frac{F^{{\left (d x + c\right )}^{n} b + a}}{b d n \log \left (F\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.53083, size = 70, normalized size = 2.59 \begin{align*} \frac{e^{\left ({\left (d x + c\right )}^{n} b \log \left (F\right ) + a \log \left (F\right )\right )}}{b d n \log \left (F\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.40768, size = 36, normalized size = 1.33 \begin{align*} \frac{F^{{\left (d x + c\right )}^{n} b + a}}{b d n \log \left (F\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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