Optimal. Leaf size=22 \[ \frac{F^a \text{Ei}\left (b (c+d x)^2 \log (F)\right )}{2 d} \]
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Rubi [A] time = 0.0676199, 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} \[ \frac{F^a \text{Ei}\left (b (c+d x)^2 \log (F)\right )}{2 d} \]
Antiderivative was successfully verified.
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Rule 2210
Rubi steps
\begin{align*} \int \frac{F^{a+b (c+d x)^2}}{c+d x} \, dx &=\frac{F^a \text{Ei}\left (b (c+d x)^2 \log (F)\right )}{2 d}\\ \end{align*}
Mathematica [A] time = 0.0062464, size = 22, normalized size = 1. \[ \frac{F^a \text{Ei}\left (b (c+d x)^2 \log (F)\right )}{2 d} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.021, size = 23, normalized size = 1.1 \begin{align*} -{\frac{{F}^{a}{\it Ei} \left ( 1,-b \left ( dx+c \right ) ^{2}\ln \left ( F \right ) \right ) }{2\,d}} \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 )}^{2} b + a}}{d x + c}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.5086, size = 73, normalized size = 3.32 \begin{align*} \frac{F^{a}{\rm Ei}\left ({\left (b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right )} \log \left (F\right )\right )}{2 \, 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 )^{2}}}{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 )}^{2} b + a}}{d x + c}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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