Optimal. Leaf size=18 \[ \frac {\text {li}(c x)}{c}-\frac {x}{\log (c x)} \]
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Rubi [A] time = 0.01, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {2297, 2298} \[ \frac {\text {li}(c x)}{c}-\frac {x}{\log (c x)} \]
Antiderivative was successfully verified.
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Rule 2297
Rule 2298
Rubi steps
\begin {align*} \int \frac {1}{\log ^2(c x)} \, dx &=-\frac {x}{\log (c x)}+\int \frac {1}{\log (c x)} \, dx\\ &=-\frac {x}{\log (c x)}+\frac {\text {li}(c x)}{c}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 18, normalized size = 1.00 \[ \frac {\text {li}(c x)}{c}-\frac {x}{\log (c x)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 25, normalized size = 1.39 \[ -\frac {c x - \log \left (c x\right ) \operatorname {log\_integral}\left (c x\right )}{c \log \left (c x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 19, normalized size = 1.06 \[ \frac {{\rm Ei}\left (\log \left (c x\right )\right )}{c} - \frac {x}{\log \left (c x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 24, normalized size = 1.33 \[ -\frac {\Ei \left (1, -\ln \left (c x \right )\right )}{c}-\frac {x}{\ln \left (c x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.91, size = 12, normalized size = 0.67 \[ \frac {\Gamma \left (-1, -\log \left (c x\right )\right )}{c} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.34, size = 18, normalized size = 1.00 \[ \frac {\mathrm {logint}\left (c\,x\right )}{c}-\frac {x}{\ln \left (c\,x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.50, size = 12, normalized size = 0.67 \[ - \frac {x}{\log {\left (c x \right )}} + \frac {\operatorname {li}{\left (c x \right )}}{c} \]
Verification of antiderivative is not currently implemented for this CAS.
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