Optimal. Leaf size=20 \[ \frac{F^{c (a+b x)}}{b c \log (F)} \]
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Rubi [A] time = 0.0036889, antiderivative size = 20, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0048603, 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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Maple [A] time = 0.001, size = 21, normalized size = 1.1 \begin{align*}{\frac{{F}^{c \left ( bx+a \right ) }}{bc\ln \left ( F \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.944983, size = 27, normalized size = 1.35 \begin{align*} \frac{F^{{\left (b x + a\right )} c}}{b c \log \left (F\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.51071, size = 41, normalized size = 2.05 \begin{align*} \frac{F^{b c x + a c}}{b c \log \left (F\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.108263, size = 20, normalized size = 1. \begin{align*} \begin{cases} \frac{F^{c \left (a + b x\right )}}{b c \log{\left (F \right )}} & \text{for}\: b c \log{\left (F \right )} \neq 0 \\x & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.58521, size = 27, normalized size = 1.35 \begin{align*} \frac{F^{{\left (b x + a\right )} c}}{b c \log \left (F\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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