Optimal. Leaf size=32 \[ -\frac {\log ^2(c x)}{2 x^2}-\frac {\log (c x)}{2 x^2}-\frac {1}{4 x^2} \]
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Rubi [A] time = 0.02, antiderivative size = 32, 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} \[ -\frac {\log ^2(c x)}{2 x^2}-\frac {\log (c x)}{2 x^2}-\frac {1}{4 x^2} \]
Antiderivative was successfully verified.
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Rule 2304
Rule 2305
Rubi steps
\begin {align*} \int \frac {\log ^2(c x)}{x^3} \, dx &=-\frac {\log ^2(c x)}{2 x^2}+\int \frac {\log (c x)}{x^3} \, dx\\ &=-\frac {1}{4 x^2}-\frac {\log (c x)}{2 x^2}-\frac {\log ^2(c x)}{2 x^2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 32, normalized size = 1.00 \[ -\frac {\log ^2(c x)}{2 x^2}-\frac {\log (c x)}{2 x^2}-\frac {1}{4 x^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 21, normalized size = 0.66 \[ -\frac {2 \, \log \left (c x\right )^{2} + 2 \, \log \left (c x\right ) + 1}{4 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 26, normalized size = 0.81 \[ -\frac {\log \left (c x\right )^{2}}{2 \, x^{2}} - \frac {\log \left (c x\right )}{2 \, x^{2}} - \frac {1}{4 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 27, normalized size = 0.84 \[ -\frac {\ln \left (c x \right )^{2}}{2 x^{2}}-\frac {\ln \left (c x \right )}{2 x^{2}}-\frac {1}{4 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 21, normalized size = 0.66 \[ -\frac {2 \, \log \left (c x\right )^{2} + 2 \, \log \left (c x\right ) + 1}{4 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.38, size = 21, normalized size = 0.66 \[ -\frac {\frac {{\ln \left (c\,x\right )}^2}{2}+\frac {\ln \left (c\,x\right )}{2}+\frac {1}{4}}{x^2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 29, normalized size = 0.91 \[ - \frac {\log {\left (c x \right )}^{2}}{2 x^{2}} - \frac {\log {\left (c x \right )}}{2 x^{2}} - \frac {1}{4 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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