Optimal. Leaf size=30 \[ a x+\frac {b \left (F^{g (e+f x)}\right )^n}{f g n \log (F)} \]
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Rubi [A] time = 0.02, antiderivative size = 30, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {2194} \[ a x+\frac {b \left (F^{g (e+f x)}\right )^n}{f g n \log (F)} \]
Antiderivative was successfully verified.
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Rule 2194
Rubi steps
\begin {align*} \int \left (a+b \left (F^{g (e+f x)}\right )^n\right ) \, dx &=a x+b \int \left (F^{g (e+f x)}\right )^n \, dx\\ &=a x+\frac {b \left (F^{g (e+f x)}\right )^n}{f g n \log (F)}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 30, normalized size = 1.00 \[ a x+\frac {b \left (F^{g (e+f x)}\right )^n}{f g n \log (F)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.47, size = 37, normalized size = 1.23 \[ \frac {a f g n x \log \relax (F) + F^{f g n x + e g n} b}{f g n \log \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 32, normalized size = 1.07 \[ a x + \frac {F^{f g n x + g n e} b}{f g n \log \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 31, normalized size = 1.03 \[ a x +\frac {b \left (F^{\left (f x +e \right ) g}\right )^{n}}{f g n \ln \relax (F )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.93, size = 31, normalized size = 1.03 \[ a x + \frac {{\left (F^{f g x + e g}\right )}^{n} b}{f g n \log \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.60, size = 31, normalized size = 1.03 \[ a\,x+\frac {b\,{\left (F^{e\,g+f\,g\,x}\right )}^n}{f\,g\,n\,\ln \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 32, normalized size = 1.07 \[ a x + \begin {cases} \frac {b \left (F^{g \left (e + f x\right )}\right )^{n}}{f g n \log {\relax (F )}} & \text {for}\: f g n \log {\relax (F )} \neq 0 \\b x & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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