Optimal. Leaf size=26 \[ -\frac {\log ^2(c x)}{x}-\frac {2 \log (c x)}{x}-\frac {2}{x} \]
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Rubi [A] time = 0.02, antiderivative size = 26, 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 = {2305, 2304} \[ -\frac {\log ^2(c x)}{x}-\frac {2 \log (c x)}{x}-\frac {2}{x} \]
Antiderivative was successfully verified.
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Rule 2304
Rule 2305
Rubi steps
\begin {align*} \int \frac {\log ^2(c x)}{x^2} \, dx &=-\frac {\log ^2(c x)}{x}+2 \int \frac {\log (c x)}{x^2} \, dx\\ &=-\frac {2}{x}-\frac {2 \log (c x)}{x}-\frac {\log ^2(c x)}{x}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 26, normalized size = 1.00 \[ -\frac {\log ^2(c x)}{x}-\frac {2 \log (c x)}{x}-\frac {2}{x} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.45, size = 19, normalized size = 0.73 \[ -\frac {\log \left (c x\right )^{2} + 2 \, \log \left (c x\right ) + 2}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 26, normalized size = 1.00 \[ -\frac {\log \left (c x\right )^{2}}{x} - \frac {2 \, \log \left (c x\right )}{x} - \frac {2}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 27, normalized size = 1.04 \[ -\frac {\ln \left (c x \right )^{2}}{x}-\frac {2 \ln \left (c x \right )}{x}-\frac {2}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 19, normalized size = 0.73 \[ -\frac {\log \left (c x\right )^{2} + 2 \, \log \left (c x\right ) + 2}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.59, size = 19, normalized size = 0.73 \[ -\frac {{\ln \left (c\,x\right )}^2+2\,\ln \left (c\,x\right )+2}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 20, normalized size = 0.77 \[ - \frac {\log {\left (c x \right )}^{2}}{x} - \frac {2 \log {\left (c x \right )}}{x} - \frac {2}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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