Optimal. Leaf size=22 \[ \frac {F^a \text {Ei}\left (b (c+d x)^n \log (F)\right )}{d n} \]
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Rubi [A] time = 0.03, 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} \[ \frac {F^a \text {Ei}\left (b (c+d x)^n \log (F)\right )}{d n} \]
Antiderivative was successfully verified.
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Rule 2210
Rubi steps
\begin {align*} \int \frac {F^{a+b (c+d x)^n}}{c+d x} \, dx &=\frac {F^a \text {Ei}\left (b (c+d x)^n \log (F)\right )}{d n}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 22, normalized size = 1.00 \[ \frac {F^a \text {Ei}\left (b (c+d x)^n \log (F)\right )}{d n} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 22, normalized size = 1.00 \[ \frac {F^{a} {\rm Ei}\left ({\left (d x + c\right )}^{n} b \log \relax (F)\right )}{d n} \]
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 \[ \int \frac {F^{{\left (d x + c\right )}^{n} b + a}}{d x + c}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.34, size = 26, normalized size = 1.18 \[ -\frac {F^{a} \Ei \left (1, -b \left (d x +c \right )^{n} \ln \relax (F )\right )}{d n} \]
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 \[ \int \frac {F^{{\left (d x + c\right )}^{n} b + a}}{d x + c}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {F^a\,F^{b\,{\left (c+d\,x\right )}^n}}{c+d\,x} \,d x \]
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 \[ \int \frac {F^{a + b \left (c + d x\right )^{n}}}{c + d x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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