Optimal. Leaf size=23 \[ \frac{\log \left (a+b F^{c+d x}\right )}{b d \log (F)} \]
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Rubi [A] time = 0.036539, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.095, Rules used = {2246, 31} \[ \frac{\log \left (a+b F^{c+d x}\right )}{b d \log (F)} \]
Antiderivative was successfully verified.
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Rule 2246
Rule 31
Rubi steps
\begin{align*} \int \frac{F^{c+d x}}{a+b F^{c+d x}} \, dx &=\frac{\operatorname{Subst}\left (\int \frac{1}{a+b x} \, dx,x,F^{c+d x}\right )}{d \log (F)}\\ &=\frac{\log \left (a+b F^{c+d x}\right )}{b d \log (F)}\\ \end{align*}
Mathematica [A] time = 0.0071278, size = 23, normalized size = 1. \[ \frac{\log \left (a+b F^{c+d x}\right )}{b d \log (F)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 24, normalized size = 1. \begin{align*}{\frac{\ln \left ( a+b{F}^{dx+c} \right ) }{bd\ln \left ( F \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.05933, size = 31, normalized size = 1.35 \begin{align*} \frac{\log \left (F^{d x + c} b + a\right )}{b d \log \left (F\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.5073, size = 50, normalized size = 2.17 \begin{align*} \frac{\log \left (F^{d x + c} b + a\right )}{b d \log \left (F\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.133404, size = 17, normalized size = 0.74 \begin{align*} \frac{\log{\left (F^{c + d x} + \frac{a}{b} \right )}}{b d \log{\left (F \right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.28795, size = 32, normalized size = 1.39 \begin{align*} \frac{\log \left ({\left | F^{d x + c} b + a \right |}\right )}{b d \log \left (F\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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