Optimal. Leaf size=18 \[ \frac {x^2}{\log ^2\left (-2+(3+\log (9+\log (5)))^2\right )} \]
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Rubi [A] time = 0.01, antiderivative size = 23, normalized size of antiderivative = 1.28, number of steps used = 2, number of rules used = 2, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {12, 30} \begin {gather*} \frac {x^2}{\log ^2\left (7+\log ^2(9+\log (5))+6 \log (9+\log (5))\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {2 \int x \, dx}{\log ^2\left (7+6 \log (9+\log (5))+\log ^2(9+\log (5))\right )}\\ &=\frac {x^2}{\log ^2\left (7+6 \log (9+\log (5))+\log ^2(9+\log (5))\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 23, normalized size = 1.28 \begin {gather*} \frac {x^2}{\log ^2\left (7+6 \log (9+\log (5))+\log ^2(9+\log (5))\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.58, size = 23, normalized size = 1.28 \begin {gather*} \frac {x^{2}}{\log \left (\log \left (\log \relax (5) + 9\right )^{2} + 6 \, \log \left (\log \relax (5) + 9\right ) + 7\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 23, normalized size = 1.28 \begin {gather*} \frac {x^{2}}{\log \left (\log \left (\log \relax (5) + 9\right )^{2} + 6 \, \log \left (\log \relax (5) + 9\right ) + 7\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 24, normalized size = 1.33
method | result | size |
gosper | \(\frac {x^{2}}{\ln \left (\ln \left (\ln \relax (5)+9\right )^{2}+6 \ln \left (\ln \relax (5)+9\right )+7\right )^{2}}\) | \(24\) |
default | \(\frac {x^{2}}{\ln \left (\ln \left (\ln \relax (5)+9\right )^{2}+6 \ln \left (\ln \relax (5)+9\right )+7\right )^{2}}\) | \(24\) |
norman | \(\frac {x^{2}}{\ln \left (\ln \left (\ln \relax (5)+9\right )^{2}+6 \ln \left (\ln \relax (5)+9\right )+7\right )^{2}}\) | \(24\) |
risch | \(\frac {x^{2}}{\ln \left (\ln \left (\ln \relax (5)+9\right )^{2}+6 \ln \left (\ln \relax (5)+9\right )+7\right )^{2}}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 23, normalized size = 1.28 \begin {gather*} \frac {x^{2}}{\log \left (\log \left (\log \relax (5) + 9\right )^{2} + 6 \, \log \left (\log \relax (5) + 9\right ) + 7\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.25, size = 23, normalized size = 1.28 \begin {gather*} \frac {x^2}{{\ln \left (6\,\ln \left (\ln \relax (5)+9\right )+{\ln \left (\ln \relax (5)+9\right )}^2+7\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 24, normalized size = 1.33 \begin {gather*} \frac {x^{2}}{\log {\left (\log {\left (\log {\relax (5 )} + 9 \right )}^{2} + 7 + 6 \log {\left (\log {\relax (5 )} + 9 \right )} \right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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