Optimal. Leaf size=16 \[ \frac {8 \left (-x+\log ^2(\log (x))\right )}{5 x^2} \]
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Rubi [F] time = 0.26, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {8 x \log (x)+16 \log (\log (x))-16 \log (x) \log ^2(\log (x))}{5 x^3 \log (x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \frac {8 x \log (x)+16 \log (\log (x))-16 \log (x) \log ^2(\log (x))}{x^3 \log (x)} \, dx\\ &=\frac {1}{5} \int \frac {8 \left (x \log (x)+2 \log (\log (x))-2 \log (x) \log ^2(\log (x))\right )}{x^3 \log (x)} \, dx\\ &=\frac {8}{5} \int \frac {x \log (x)+2 \log (\log (x))-2 \log (x) \log ^2(\log (x))}{x^3 \log (x)} \, dx\\ &=\frac {8}{5} \int \left (\frac {1}{x^2}+\frac {2 \log (\log (x))}{x^3 \log (x)}-\frac {2 \log ^2(\log (x))}{x^3}\right ) \, dx\\ &=-\frac {8}{5 x}+\frac {16}{5} \int \frac {\log (\log (x))}{x^3 \log (x)} \, dx-\frac {16}{5} \int \frac {\log ^2(\log (x))}{x^3} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.07, size = 20, normalized size = 1.25 \begin {gather*} -\frac {8}{5 x}+\frac {8 \log ^2(\log (x))}{5 x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.72, size = 14, normalized size = 0.88 \begin {gather*} \frac {8 \, {\left (\log \left (\log \relax (x)\right )^{2} - x\right )}}{5 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.40, size = 16, normalized size = 1.00 \begin {gather*} \frac {8 \, \log \left (\log \relax (x)\right )^{2}}{5 \, x^{2}} - \frac {8}{5 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 17, normalized size = 1.06
method | result | size |
risch | \(\frac {8 \ln \left (\ln \relax (x )\right )^{2}}{5 x^{2}}-\frac {8}{5 x}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 16, normalized size = 1.00 \begin {gather*} \frac {8 \, \log \left (\log \relax (x)\right )^{2}}{5 \, x^{2}} - \frac {8}{5 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.96, size = 14, normalized size = 0.88 \begin {gather*} -\frac {8\,\left (x-{\ln \left (\ln \relax (x)\right )}^2\right )}{5\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.28, size = 17, normalized size = 1.06 \begin {gather*} - \frac {8}{5 x} + \frac {8 \log {\left (\log {\relax (x )} \right )}^{2}}{5 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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