Optimal. Leaf size=21 \[ \log ^2\left (2+\frac {1}{2} (1+\log (4))-\log (\log (-1+\log (x)))\right ) \]
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Rubi [A] time = 0.31, antiderivative size = 19, normalized size of antiderivative = 0.90, number of steps used = 3, number of rules used = 3, integrand size = 69, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {12, 6684, 6686} \begin {gather*} \log ^2\left (\frac {1}{2} (-2 \log (\log (\log (x)-1))+5+\log (4))\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6684
Rule 6686
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=4 \int \frac {\log \left (\frac {1}{2} (5+\log (4)-2 \log (\log (-1+\log (x))))\right )}{(5 x+x \log (4)+(-5 x-x \log (4)) \log (x)) \log (-1+\log (x))+(-2 x+2 x \log (x)) \log (-1+\log (x)) \log (\log (-1+\log (x)))} \, dx\\ &=-\left (4 \operatorname {Subst}\left (\int \frac {\log \left (\frac {1}{2} (5+\log (4)-2 \log (\log (-1+x)))\right )}{(-1+x) \log (-1+x) (5+\log (4)-2 \log (\log (-1+x)))} \, dx,x,\log (x)\right )\right )\\ &=\log ^2\left (\frac {1}{2} (5+\log (4)-2 \log (\log (-1+\log (x))))\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.05, size = 24, normalized size = 1.14 \begin {gather*} \log ^2\left (\frac {5}{2} \left (1+\frac {2 \log (2)}{5}\right )-\log (\log (-1+\log (x)))\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.66, size = 15, normalized size = 0.71 \begin {gather*} \log \left (\log \relax (2) - \log \left (\log \left (\log \relax (x) - 1\right )\right ) + \frac {5}{2}\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 15, normalized size = 0.71 \begin {gather*} \log \left (\log \relax (2) - \log \left (\log \left (\log \relax (x) - 1\right )\right ) + \frac {5}{2}\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 16, normalized size = 0.76
method | result | size |
risch | \(\ln \left (-\ln \left (\ln \left (\ln \relax (x )-1\right )\right )+\ln \relax (2)+\frac {5}{2}\right )^{2}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.46, size = 50, normalized size = 2.38 \begin {gather*} 2 \, \log \left (\log \relax (2) - \log \left (\log \left (\log \relax (x) - 1\right )\right ) + \frac {5}{2}\right ) \log \left (-2 \, \log \relax (2) + 2 \, \log \left (\log \left (\log \relax (x) - 1\right )\right ) - 5\right ) - \log \left (-2 \, \log \relax (2) + 2 \, \log \left (\log \left (\log \relax (x) - 1\right )\right ) - 5\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {4\,\ln \left (\ln \relax (2)-\ln \left (\ln \left (\ln \relax (x)-1\right )\right )+\frac {5}{2}\right )}{\ln \left (\ln \relax (x)-1\right )\,\left (5\,x+2\,x\,\ln \relax (2)-\ln \relax (x)\,\left (5\,x+2\,x\,\ln \relax (2)\right )\right )-\ln \left (\ln \left (\ln \relax (x)-1\right )\right )\,\ln \left (\ln \relax (x)-1\right )\,\left (2\,x-2\,x\,\ln \relax (x)\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 4.45, size = 17, normalized size = 0.81 \begin {gather*} \log {\left (- \log {\left (\log {\left (\log {\relax (x )} - 1 \right )} \right )} + \log {\relax (2 )} + \frac {5}{2} \right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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