Optimal. Leaf size=22 \[ -\frac {F^a \text {Ei}\left (\frac {b \log (F)}{(c+d x)^3}\right )}{3 d} \]
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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} \[ -\frac {F^a \text {Ei}\left (\frac {b \log (F)}{(c+d x)^3}\right )}{3 d} \]
Antiderivative was successfully verified.
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Rule 2210
Rubi steps
\begin {align*} \int \frac {F^{a+\frac {b}{(c+d x)^3}}}{c+d x} \, dx &=-\frac {F^a \text {Ei}\left (\frac {b \log (F)}{(c+d x)^3}\right )}{3 d}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 22, normalized size = 1.00 \[ -\frac {F^a \text {Ei}\left (\frac {b \log (F)}{(c+d x)^3}\right )}{3 d} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.43, size = 42, normalized size = 1.91 \[ -\frac {F^{a} {\rm Ei}\left (\frac {b \log \relax (F)}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right )}{3 \, d} \]
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 \[ \int \frac {F^{a + \frac {b}{{\left (d x + c\right )}^{3}}}}{d x + c}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.10, size = 0, normalized size = 0.00 \[ \int \frac {F^{a +\frac {b}{\left (d x +c \right )^{3}}}}{d x +c}\, dx \]
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 \[ \int \frac {F^{a + \frac {b}{{\left (d x + c\right )}^{3}}}}{d x + c}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.72, size = 20, normalized size = 0.91 \[ -\frac {F^a\,\mathrm {ei}\left (\frac {b\,\ln \relax (F)}{{\left (c+d\,x\right )}^3}\right )}{3\,d} \]
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 \[ \int \frac {F^{a + \frac {b}{\left (c + d x\right )^{3}}}}{c + d x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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