Optimal. Leaf size=16 \[ \frac{\log \left (a+b F^x\right )}{b \log (F)} \]
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Rubi [A] time = 0.0205769, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {2246, 31} \[ \frac{\log \left (a+b F^x\right )}{b \log (F)} \]
Antiderivative was successfully verified.
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Rule 2246
Rule 31
Rubi steps
\begin{align*} \int \frac{F^x}{a+b F^x} \, dx &=\frac{\operatorname{Subst}\left (\int \frac{1}{a+b x} \, dx,x,F^x\right )}{\log (F)}\\ &=\frac{\log \left (a+b F^x\right )}{b \log (F)}\\ \end{align*}
Mathematica [A] time = 0.0059151, size = 16, normalized size = 1. \[ \frac{\log \left (a+b F^x\right )}{b \log (F)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 17, normalized size = 1.1 \begin{align*}{\frac{\ln \left ( a+b{F}^{x} \right ) }{b\ln \left ( F \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.15051, size = 22, normalized size = 1.38 \begin{align*} \frac{\log \left (F^{x} b + a\right )}{b \log \left (F\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.4996, size = 36, normalized size = 2.25 \begin{align*} \frac{\log \left (F^{x} b + a\right )}{b \log \left (F\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.127843, size = 12, normalized size = 0.75 \begin{align*} \frac{\log{\left (F^{x} + \frac{a}{b} \right )}}{b \log{\left (F \right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.28401, size = 23, normalized size = 1.44 \begin{align*} \frac{\log \left ({\left | F^{x} b + a \right |}\right )}{b \log \left (F\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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