Optimal. Leaf size=27 \[ \frac{F^{a+b (c+d x)^2}}{2 b d \log (F)} \]
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Rubi [A] time = 0.0362265, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053, Rules used = {2209} \[ \frac{F^{a+b (c+d x)^2}}{2 b d \log (F)} \]
Antiderivative was successfully verified.
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Rule 2209
Rubi steps
\begin{align*} \int F^{a+b (c+d x)^2} (c+d x) \, dx &=\frac{F^{a+b (c+d x)^2}}{2 b d \log (F)}\\ \end{align*}
Mathematica [A] time = 0.0073765, size = 27, normalized size = 1. \[ \frac{F^{a+b (c+d x)^2}}{2 b d \log (F)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 36, normalized size = 1.3 \begin{align*}{\frac{{F}^{b{d}^{2}{x}^{2}+2\,bcdx+{c}^{2}b+a}}{2\,bd\ln \left ( F \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01561, size = 34, normalized size = 1.26 \begin{align*} \frac{F^{{\left (d x + c\right )}^{2} b + a}}{2 \, b d \log \left (F\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.53574, size = 76, normalized size = 2.81 \begin{align*} \frac{F^{b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a}}{2 \, b d \log \left (F\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.136847, size = 36, normalized size = 1.33 \begin{align*} \begin{cases} \frac{F^{a + b \left (c + d x\right )^{2}}}{2 b d \log{\left (F \right )}} & \text{for}\: 2 b d \log{\left (F \right )} \neq 0 \\c x + \frac{d x^{2}}{2} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.22253, size = 34, normalized size = 1.26 \begin{align*} \frac{F^{{\left (d x + c\right )}^{2} b + a}}{2 \, b d \log \left (F\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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