Optimal. Leaf size=27 \[ \frac{F^{a+b (c+d x)^3}}{3 b d \log (F)} \]
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Rubi [A] time = 0.0672355, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.048, Rules used = {2209} \[ \frac{F^{a+b (c+d x)^3}}{3 b d \log (F)} \]
Antiderivative was successfully verified.
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Rule 2209
Rubi steps
\begin{align*} \int F^{a+b (c+d x)^3} (c+d x)^2 \, dx &=\frac{F^{a+b (c+d x)^3}}{3 b d \log (F)}\\ \end{align*}
Mathematica [A] time = 0.0084016, size = 27, normalized size = 1. \[ \frac{F^{a+b (c+d x)^3}}{3 b d \log (F)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 48, normalized size = 1.8 \begin{align*}{\frac{{F}^{b{d}^{3}{x}^{3}+3\,bc{d}^{2}{x}^{2}+3\,b{c}^{2}dx+b{c}^{3}+a}}{3\,bd\ln \left ( F \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02495, size = 34, normalized size = 1.26 \begin{align*} \frac{F^{{\left (d x + c\right )}^{3} b + a}}{3 \, 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 = 1.54858, size = 100, normalized size = 3.7 \begin{align*} \frac{F^{b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a}}{3 \, 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 = 0.159267, size = 46, normalized size = 1.7 \begin{align*} \begin{cases} \frac{F^{a + b \left (c + d x\right )^{3}}}{3 b d \log{\left (F \right )}} & \text{for}\: 3 b d \log{\left (F \right )} \neq 0 \\c^{2} x + c d x^{2} + \frac{d^{2} x^{3}}{3} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.22812, size = 34, normalized size = 1.26 \begin{align*} \frac{F^{{\left (d x + c\right )}^{3} b + a}}{3 \, b d \log \left (F\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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