Optimal. Leaf size=22 \[ -\frac{F^a \text{Ei}\left (\frac{b \log (F)}{(c+d x)^2}\right )}{2 d} \]
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Rubi [A] time = 0.0447805, 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} \[ -\frac{F^a \text{Ei}\left (\frac{b \log (F)}{(c+d x)^2}\right )}{2 d} \]
Antiderivative was successfully verified.
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Rule 2210
Rubi steps
\begin{align*} \int \frac{F^{a+\frac{b}{(c+d x)^2}}}{c+d x} \, dx &=-\frac{F^a \text{Ei}\left (\frac{b \log (F)}{(c+d x)^2}\right )}{2 d}\\ \end{align*}
Mathematica [A] time = 0.0058154, size = 22, normalized size = 1. \[ -\frac{F^a \text{Ei}\left (\frac{b \log (F)}{(c+d x)^2}\right )}{2 d} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.026, size = 23, normalized size = 1.1 \begin{align*}{\frac{{F}^{a}}{2\,d}{\it Ei} \left ( 1,-{\frac{b\ln \left ( F \right ) }{ \left ( dx+c \right ) ^{2}}} \right ) } \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 )}^{2}}}}{d x + c}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.61045, size = 69, normalized size = 3.14 \begin{align*} -\frac{F^{a}{\rm Ei}\left (\frac{b \log \left (F\right )}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right )}{2 \, d} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \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 )}^{2}}}}{d x + c}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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