Optimal. Leaf size=11 \[ \frac{\text{Ei}(4 \log (c x))}{c^4} \]
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Rubi [A] time = 0.0238933, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2, Rules used = {2309, 2178} \[ \frac{\text{Ei}(4 \log (c x))}{c^4} \]
Antiderivative was successfully verified.
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Rule 2309
Rule 2178
Rubi steps
\begin{align*} \int \frac{x^3}{\log (c x)} \, dx &=\frac{\operatorname{Subst}\left (\int \frac{e^{4 x}}{x} \, dx,x,\log (c x)\right )}{c^4}\\ &=\frac{\text{Ei}(4 \log (c x))}{c^4}\\ \end{align*}
Mathematica [A] time = 0.0143969, size = 11, normalized size = 1. \[ \frac{\text{Ei}(4 \log (c x))}{c^4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.04, size = 14, normalized size = 1.3 \begin{align*} -{\frac{{\it Ei} \left ( 1,-4\,\ln \left ( cx \right ) \right ) }{{c}^{4}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.1214, size = 15, normalized size = 1.36 \begin{align*} \frac{{\rm Ei}\left (4 \, \log \left (c x\right )\right )}{c^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.731077, size = 36, normalized size = 3.27 \begin{align*} \frac{\logintegral \left (c^{4} x^{4}\right )}{c^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x^{3}}{\log{\left (c x \right )}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13243, size = 15, normalized size = 1.36 \begin{align*} \frac{{\rm Ei}\left (4 \, \log \left (c x\right )\right )}{c^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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