Optimal. Leaf size=20 \[ \frac {F^{c (a+b x)}}{b c \log (F)} \]
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Rubi [A] time = 0.00, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {2194} \[ \frac {F^{c (a+b x)}}{b c \log (F)} \]
Antiderivative was successfully verified.
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Rule 2194
Rubi steps
\begin {align*} \int F^{c (a+b x)} \, dx &=\frac {F^{c (a+b x)}}{b c \log (F)}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 21, normalized size = 1.05 \[ \frac {F^{a c+b c x}}{b c \log (F)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.44, size = 21, normalized size = 1.05 \[ \frac {F^{b c x + a c}}{b c \log \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.31, size = 21, normalized size = 1.05 \[ \frac {F^{b c x + a c}}{b c \log \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 21, normalized size = 1.05 \[ \frac {F^{\left (b x +a \right ) c}}{b c \ln \relax (F )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 20, normalized size = 1.00 \[ \frac {F^{{\left (b x + a\right )} c}}{b c \log \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.43, size = 21, normalized size = 1.05 \[ \frac {F^{a\,c+b\,c\,x}}{b\,c\,\ln \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 20, normalized size = 1.00 \[ \begin {cases} \frac {F^{c \left (a + b x\right )}}{b c \log {\relax (F )}} & \text {for}\: b c \log {\relax (F )} \neq 0 \\x & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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