Optimal. Leaf size=49 \[ -\frac{F^a (c+d x)^4 \text{Gamma}\left (\frac{4}{3},-b \log (F) (c+d x)^3\right )}{3 d \left (-b \log (F) (c+d x)^3\right )^{4/3}} \]
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Rubi [A] time = 0.0638079, antiderivative size = 49, 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 = {2218} \[ -\frac{F^a (c+d x)^4 \text{Gamma}\left (\frac{4}{3},-b \log (F) (c+d x)^3\right )}{3 d \left (-b \log (F) (c+d x)^3\right )^{4/3}} \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin{align*} \int F^{a+b (c+d x)^3} (c+d x)^3 \, dx &=-\frac{F^a (c+d x)^4 \Gamma \left (\frac{4}{3},-b (c+d x)^3 \log (F)\right )}{3 d \left (-b (c+d x)^3 \log (F)\right )^{4/3}}\\ \end{align*}
Mathematica [A] time = 0.0253807, size = 49, normalized size = 1. \[ -\frac{F^a (c+d x)^4 \text{Gamma}\left (\frac{4}{3},-b \log (F) (c+d x)^3\right )}{3 d \left (-b \log (F) (c+d x)^3\right )^{4/3}} \]
Antiderivative was successfully verified.
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Maple [F] time = 0.047, size = 0, normalized size = 0. \begin{align*} \int{F}^{a+b \left ( dx+c \right ) ^{3}} \left ( dx+c \right ) ^{3}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int{\left (d x + c\right )}^{3} F^{{\left (d x + c\right )}^{3} b + a}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.62648, size = 282, normalized size = 5.76 \begin{align*} \frac{3 \,{\left (b d^{3} x + b c d^{2}\right )} F^{b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a} \log \left (F\right ) - \left (-b d^{3} \log \left (F\right )\right )^{\frac{2}{3}} F^{a} \Gamma \left (\frac{1}{3}, -{\left (b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3}\right )} \log \left (F\right )\right )}{9 \, b^{2} d^{3} \log \left (F\right )^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int F^{a + b \left (c + d x\right )^{3}} \left (c + d x\right )^{3}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int{\left (d x + c\right )}^{3} F^{{\left (d x + c\right )}^{3} b + a}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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