Optimal. Leaf size=23 \[ \frac {2}{-2 x+\left (3+\log ^2(4)\right )^2-\log (x \log (x))} \]
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Rubi [A] time = 0.21, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 114, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {6688, 12, 6686} \begin {gather*} -\frac {2}{2 x+\log (x \log (x))-\left (3+\log ^2(4)\right )^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6686
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 (1+\log (x)+2 x \log (x))}{x \log (x) \left (2 x-\left (3+\log ^2(4)\right )^2+\log (x \log (x))\right )^2} \, dx\\ &=2 \int \frac {1+\log (x)+2 x \log (x)}{x \log (x) \left (2 x-\left (3+\log ^2(4)\right )^2+\log (x \log (x))\right )^2} \, dx\\ &=-\frac {2}{2 x-\left (3+\log ^2(4)\right )^2+\log (x \log (x))}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 23, normalized size = 1.00 \begin {gather*} -\frac {2}{2 x-\left (3+\log ^2(4)\right )^2+\log (x \log (x))} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.97, size = 28, normalized size = 1.22 \begin {gather*} \frac {2}{16 \, \log \relax (2)^{4} + 24 \, \log \relax (2)^{2} - 2 \, x - \log \left (x \log \relax (x)\right ) + 9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.34, size = 30, normalized size = 1.30 \begin {gather*} \frac {2}{16 \, \log \relax (2)^{4} + 24 \, \log \relax (2)^{2} - 2 \, x - \log \relax (x) - \log \left (\log \relax (x)\right ) + 9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.12, size = 104, normalized size = 4.52
method | result | size |
risch | \(-\frac {4 i}{\pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (i x \ln \relax (x )\right )-\pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x \ln \relax (x )\right )^{2}-\pi \,\mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (i x \ln \relax (x )\right )^{2}+\pi \mathrm {csgn}\left (i x \ln \relax (x )\right )^{3}-32 i \ln \relax (2)^{4}-48 i \ln \relax (2)^{2}+4 i x +2 i \ln \relax (x )+2 i \ln \left (\ln \relax (x )\right )-18 i}\) | \(104\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.67, size = 30, normalized size = 1.30 \begin {gather*} \frac {2}{16 \, \log \relax (2)^{4} + 24 \, \log \relax (2)^{2} - 2 \, x - \log \relax (x) - \log \left (\log \relax (x)\right ) + 9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.84, size = 28, normalized size = 1.22 \begin {gather*} \frac {2}{24\,{\ln \relax (2)}^2-\ln \left (x\,\ln \relax (x)\right )-2\,x+16\,{\ln \relax (2)}^4+9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.40, size = 27, normalized size = 1.17 \begin {gather*} - \frac {2}{2 x + \log {\left (x \log {\relax (x )} \right )} - 24 \log {\relax (2 )}^{2} - 9 - 16 \log {\relax (2 )}^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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