Optimal. Leaf size=22 \[ \frac{F^a \text{Ei}\left (b (c+d x)^3 \log (F)\right )}{3 d} \]
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Rubi [A] time = 0.0658895, antiderivative size = 22, 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 = {2210} \[ \frac{F^a \text{Ei}\left (b (c+d x)^3 \log (F)\right )}{3 d} \]
Antiderivative was successfully verified.
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Rule 2210
Rubi steps
\begin{align*} \int \frac{F^{a+b (c+d x)^3}}{c+d x} \, dx &=\frac{F^a \text{Ei}\left (b (c+d x)^3 \log (F)\right )}{3 d}\\ \end{align*}
Mathematica [A] time = 0.0064917, size = 22, normalized size = 1. \[ \frac{F^a \text{Ei}\left (b (c+d x)^3 \log (F)\right )}{3 d} \]
Antiderivative was successfully verified.
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Maple [F] time = 0.036, size = 0, normalized size = 0. \begin{align*} \int{\frac{{F}^{a+b \left ( dx+c \right ) ^{3}}}{dx+c}}\, 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 \frac{F^{{\left (d x + c\right )}^{3} b + a}}{d x + c}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.6311, size = 97, normalized size = 4.41 \begin{align*} \frac{F^{a}{\rm Ei}\left ({\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 )}{3 \, d} \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 \frac{F^{a + b \left (c + d x\right )^{3}}}{c + d x}\, 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 \frac{F^{{\left (d x + c\right )}^{3} b + a}}{d x + c}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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