Optimal. Leaf size=20 \[ -\frac {F^a \text {Ei}\left (\frac {b \log (F)}{c+d x}\right )}{d} \]
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Rubi [A] time = 0.04, antiderivative size = 20, 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} \[ -\frac {F^a \text {Ei}\left (\frac {b \log (F)}{c+d x}\right )}{d} \]
Antiderivative was successfully verified.
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Rule 2210
Rubi steps
\begin {align*} \int \frac {F^{a+\frac {b}{c+d x}}}{c+d x} \, dx &=-\frac {F^a \text {Ei}\left (\frac {b \log (F)}{c+d x}\right )}{d}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 20, normalized size = 1.00 \[ -\frac {F^a \text {Ei}\left (\frac {b \log (F)}{c+d x}\right )}{d} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 20, normalized size = 1.00 \[ -\frac {F^{a} {\rm Ei}\left (\frac {b \log \relax (F)}{d x + c}\right )}{d} \]
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 \[ \int \frac {F^{a + \frac {b}{d x + c}}}{d x + c}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.12, size = 22, normalized size = 1.10 \[ \frac {F^{a} \Ei \left (1, -\frac {b \ln \relax (F )}{d x +c}\right )}{d} \]
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 \[ \int \frac {F^{a + \frac {b}{d x + c}}}{d x + c}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.76, size = 20, normalized size = 1.00 \[ -\frac {F^a\,\mathrm {ei}\left (\frac {b\,\ln \relax (F)}{c+d\,x}\right )}{d} \]
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 \[ \int \frac {F^{a + \frac {b}{c + d x}}}{c + d x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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