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 = 0.0211592, antiderivative size = 32, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2, 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 2305
Rule 2304
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*}
Mathematica [A] time = 0.001618, size = 32, normalized size = 1. \[ -\frac{1}{32 x^4}-\frac{\log ^2\left (\frac{1}{x}\right )}{4 x^4}+\frac{\log \left (\frac{1}{x}\right )}{8 x^4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 27, normalized size = 0.8 \begin{align*} -{\frac{1}{32\,{x}^{4}}}+{\frac{\ln \left ({x}^{-1} \right ) }{8\,{x}^{4}}}-{\frac{ \left ( \ln \left ({x}^{-1} \right ) \right ) ^{2}}{4\,{x}^{4}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.993019, size = 23, normalized size = 0.72 \begin{align*} -\frac{8 \, \log \left (x\right )^{2} + 4 \, \log \left (x\right ) + 1}{32 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.75354, size = 58, normalized size = 1.81 \begin{align*} -\frac{8 \, \log \left (\frac{1}{x}\right )^{2} - 4 \, \log \left (\frac{1}{x}\right ) + 1}{32 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.131458, size = 27, normalized size = 0.84 \begin{align*} - \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}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.35236, size = 30, normalized size = 0.94 \begin{align*} -\frac{\log \left (x\right )^{2}}{4 \, x^{4}} - \frac{\log \left (x\right )}{8 \, x^{4}} - \frac{1}{32 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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