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 = 0.07, antiderivative size = 22, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.01, size = 22, normalized size = 1.00 \[ \frac {F^a \text {Ei}\left (b (c+d x)^2 \log (F)\right )}{2 d} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.52, size = 32, normalized size = 1.45 \[ \frac {F^{a} {\rm Ei}\left ({\left (b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right )} \log \relax (F)\right )}{2 \, d} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {F^{{\left (d x + c\right )}^{2} b + a}}{d x + c}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 23, normalized size = 1.05 \[ -\frac {F^{a} \Ei \left (1, -\left (d x +c \right )^{2} b \ln \relax (F )\right )}{2 d} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {F^{{\left (d x + c\right )}^{2} b + a}}{d x + c}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.68, size = 20, normalized size = 0.91 \[ \frac {F^a\,\mathrm {ei}\left (b\,\ln \relax (F)\,{\left (c+d\,x\right )}^2\right )}{2\,d} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {F^{a + b \left (c + d x\right )^{2}}}{c + d x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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