Optimal. Leaf size=11 \[ \frac {\text {Ei}(3 \log (c x))}{c^3} \]
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Rubi [A] time = 0.02, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {2309, 2178} \[ \frac {\text {Ei}(3 \log (c x))}{c^3} \]
Antiderivative was successfully verified.
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Rule 2178
Rule 2309
Rubi steps
\begin {align*} \int \frac {x^2}{\log (c x)} \, dx &=\frac {\operatorname {Subst}\left (\int \frac {e^{3 x}}{x} \, dx,x,\log (c x)\right )}{c^3}\\ &=\frac {\text {Ei}(3 \log (c x))}{c^3}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 11, normalized size = 1.00 \[ \frac {\text {Ei}(3 \log (c x))}{c^3} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 12, normalized size = 1.09 \[ \frac {\operatorname {log\_integral}\left (c^{3} x^{3}\right )}{c^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.24, size = 11, normalized size = 1.00 \[ \frac {{\rm Ei}\left (3 \, \log \left (c x\right )\right )}{c^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 14, normalized size = 1.27 \[ -\frac {\Ei \left (1, -3 \ln \left (c x \right )\right )}{c^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.87, size = 11, normalized size = 1.00 \[ \frac {{\rm Ei}\left (3 \, \log \left (c x\right )\right )}{c^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.09 \[ \int \frac {x^2}{\ln \left (c\,x\right )} \,d x \]
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 \[ \int \frac {x^{2}}{\log {\left (c x \right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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