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 = 0.04, 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} \[ -\frac {F^a \text {Ei}\left (\frac {b \log (F)}{(c+d x)^2}\right )}{2 d} \]
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*}
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Mathematica [A] time = 0.01, size = 22, normalized size = 1.00 \[ -\frac {F^a \text {Ei}\left (\frac {b \log (F)}{(c+d x)^2}\right )}{2 d} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 31, normalized size = 1.41 \[ -\frac {F^{a} {\rm Ei}\left (\frac {b \log \relax (F)}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right )}{2 \, d} \]
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 \[ \int \frac {F^{a + \frac {b}{{\left (d x + c\right )}^{2}}}}{d x + c}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 23, normalized size = 1.05 \[ \frac {F^{a} \Ei \left (1, -\frac {b \ln \relax (F )}{\left (d x +c \right )^{2}}\right )}{2 d} \]
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 \[ \int \frac {F^{a + \frac {b}{{\left (d x + c\right )}^{2}}}}{d x + c}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.70, size = 20, normalized size = 0.91 \[ -\frac {F^a\,\mathrm {ei}\left (\frac {b\,\ln \relax (F)}{{\left (c+d\,x\right )}^2}\right )}{2\,d} \]
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 \[ \int \frac {F^{a + \frac {b}{\left (c + d x\right )^{2}}}}{c + d x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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