Optimal. Leaf size=22 \[ -\frac{F^a \text{Ei}\left (\frac{b \log (F)}{(c+d x)^3}\right )}{3 d} \]
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Rubi [A] time = 0.0435177, 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} \[ -\frac{F^a \text{Ei}\left (\frac{b \log (F)}{(c+d x)^3}\right )}{3 d} \]
Antiderivative was successfully verified.
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Rule 2210
Rubi steps
\begin{align*} \int \frac{F^{a+\frac{b}{(c+d x)^3}}}{c+d x} \, dx &=-\frac{F^a \text{Ei}\left (\frac{b \log (F)}{(c+d x)^3}\right )}{3 d}\\ \end{align*}
Mathematica [A] time = 0.0068292, size = 22, normalized size = 1. \[ -\frac{F^a \text{Ei}\left (\frac{b \log (F)}{(c+d x)^3}\right )}{3 d} \]
Antiderivative was successfully verified.
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Maple [F] time = 0.048, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{dx+c}{F}^{a+{\frac{b}{ \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 \frac{F^{a + \frac{b}{{\left (d x + c\right )}^{3}}}}{d x + c}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.62323, size = 90, normalized size = 4.09 \begin{align*} -\frac{F^{a}{\rm Ei}\left (\frac{b \log \left (F\right )}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\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 + \frac{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^{a + \frac{b}{{\left (d x + c\right )}^{3}}}}{d x + c}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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