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 = 0.04, antiderivative size = 23, normalized size of antiderivative = 1.00, 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 31
Rule 2246
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*}
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Mathematica [A] time = 0.01, size = 23, normalized size = 1.00 \[ \frac {\log \left (a+b F^{c+d x}\right )}{b d \log (F)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 23, normalized size = 1.00 \[ \frac {\log \left (F^{d x + c} b + a\right )}{b d \log \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.41, size = 24, normalized size = 1.04 \[ \frac {\log \left ({\left | F^{d x + c} b + a \right |}\right )}{b d \log \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 24, normalized size = 1.04 \[ \frac {\ln \left (b \,F^{d x +c}+a \right )}{b d \ln \relax (F )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 23, normalized size = 1.00 \[ \frac {\log \left (F^{d x + c} b + a\right )}{b d \log \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.00, size = 23, normalized size = 1.00 \[ \frac {\ln \left (a+F^{c+d\,x}\,b\right )}{b\,d\,\ln \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 17, normalized size = 0.74 \[ \frac {\log {\left (F^{c + d x} + \frac {a}{b} \right )}}{b d \log {\relax (F )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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