Optimal. Leaf size=32 \[ -\frac {1}{32 x^4}-\frac {\log ^2\left (\frac {1}{x}\right )}{4 x^4}+\frac {\log \left (\frac {1}{x}\right )}{8 x^4} \]
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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} \[ -\frac {1}{32 x^4}-\frac {\log ^2\left (\frac {1}{x}\right )}{4 x^4}+\frac {\log \left (\frac {1}{x}\right )}{8 x^4} \]
Antiderivative was successfully verified.
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Rule 2304
Rule 2305
Rubi steps
\begin {align*} \int \frac {\log ^2\left (\frac {1}{x}\right )}{x^5} \, dx &=-\frac {\log ^2\left (\frac {1}{x}\right )}{4 x^4}-\frac {1}{2} \int \frac {\log \left (\frac {1}{x}\right )}{x^5} \, dx\\ &=-\frac {1}{32 x^4}+\frac {\log \left (\frac {1}{x}\right )}{8 x^4}-\frac {\log ^2\left (\frac {1}{x}\right )}{4 x^4}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 32, normalized size = 1.00 \[ -\frac {1}{32 x^4}-\frac {\log ^2\left (\frac {1}{x}\right )}{4 x^4}+\frac {\log \left (\frac {1}{x}\right )}{8 x^4} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.44, size = 21, normalized size = 0.66 \[ -\frac {8 \, \log \left (\frac {1}{x}\right )^{2} - 4 \, \log \left (\frac {1}{x}\right ) + 1}{32 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 22, normalized size = 0.69 \[ -\frac {\log \relax (x)^{2}}{4 \, x^{4}} - \frac {\log \relax (x)}{8 \, x^{4}} - \frac {1}{32 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 27, normalized size = 0.84 \[ -\frac {\ln \left (\frac {1}{x}\right )^{2}}{4 x^{4}}+\frac {\ln \left (\frac {1}{x}\right )}{8 x^{4}}-\frac {1}{32 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.68, size = 17, normalized size = 0.53 \[ -\frac {8 \, \log \relax (x)^{2} + 4 \, \log \relax (x) + 1}{32 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.41, size = 21, normalized size = 0.66 \[ -\frac {\frac {{\ln \left (\frac {1}{x}\right )}^2}{4}-\frac {\ln \left (\frac {1}{x}\right )}{8}+\frac {1}{32}}{x^4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 27, normalized size = 0.84 \[ - \frac {\log {\left (\frac {1}{x} \right )}^{2}}{4 x^{4}} + \frac {\log {\left (\frac {1}{x} \right )}}{8 x^{4}} - \frac {1}{32 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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