Optimal. Leaf size=15 \[ \frac {1}{32} \left (-5 x+\frac {16}{\log (\log (x))}\right ) \]
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Rubi [A] time = 0.17, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 4, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 6688, 2302, 30} \begin {gather*} \frac {1}{2 \log (\log (x))}-\frac {5 x}{32} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rule 2302
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{32} \int \frac {-16-5 x \log (x) \log ^2(\log (x))}{x \log (x) \log ^2(\log (x))} \, dx\\ &=\frac {1}{32} \int \left (-5-\frac {16}{x \log (x) \log ^2(\log (x))}\right ) \, dx\\ &=-\frac {5 x}{32}-\frac {1}{2} \int \frac {1}{x \log (x) \log ^2(\log (x))} \, dx\\ &=-\frac {5 x}{32}-\frac {1}{2} \operatorname {Subst}\left (\int \frac {1}{x \log ^2(x)} \, dx,x,\log (x)\right )\\ &=-\frac {5 x}{32}-\frac {1}{2} \operatorname {Subst}\left (\int \frac {1}{x^2} \, dx,x,\log (\log (x))\right )\\ &=-\frac {5 x}{32}+\frac {1}{2 \log (\log (x))}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 15, normalized size = 1.00 \begin {gather*} -\frac {5 x}{32}+\frac {1}{2 \log (\log (x))} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.88, size = 15, normalized size = 1.00 \begin {gather*} -\frac {5 \, x \log \left (\log \relax (x)\right ) - 16}{32 \, \log \left (\log \relax (x)\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.24, size = 11, normalized size = 0.73 \begin {gather*} -\frac {5}{32} \, x + \frac {1}{2 \, \log \left (\log \relax (x)\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 12, normalized size = 0.80
method | result | size |
default | \(-\frac {5 x}{32}+\frac {1}{2 \ln \left (\ln \relax (x )\right )}\) | \(12\) |
risch | \(-\frac {5 x}{32}+\frac {1}{2 \ln \left (\ln \relax (x )\right )}\) | \(12\) |
norman | \(\frac {\frac {1}{2}-\frac {5 x \ln \left (\ln \relax (x )\right )}{32}}{\ln \left (\ln \relax (x )\right )}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.45, size = 11, normalized size = 0.73 \begin {gather*} -\frac {5}{32} \, x + \frac {1}{2 \, \log \left (\log \relax (x)\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.25, size = 11, normalized size = 0.73 \begin {gather*} \frac {1}{2\,\ln \left (\ln \relax (x)\right )}-\frac {5\,x}{32} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.22, size = 12, normalized size = 0.80 \begin {gather*} - \frac {5 x}{32} + \frac {1}{2 \log {\left (\log {\relax (x )} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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