Optimal. Leaf size=31 \[ \log \left (\log \left (x \left (x-\log \left (x-x \left (x+x^2 \left (-\frac {3}{x}+2 x\right ) \log (3)\right )\right )\right )\right )\right ) \]
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Rubi [A]
time = 0.12, antiderivative size = 31, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 172, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.006, Rules used = {6816}
\begin {gather*} \log \left (\log \left (x^2-x \log \left (-x^2+\left (3 x^2-2 x^4\right ) \log (3)+x\right )\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6816
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log \left (\log \left (x^2-x \log \left (x-x^2+\left (3 x^2-2 x^4\right ) \log (3)\right )\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [F]
time = 0.12, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {-1+4 x-2 x^2+\left (-6 x+6 x^2+8 x^3-4 x^4\right ) \log (3)+\left (-1+x+\left (-3 x+2 x^3\right ) \log (3)\right ) \log \left (x-x^2+\left (3 x^2-2 x^4\right ) \log (3)\right )}{\left (x^2-x^3+\left (3 x^3-2 x^5\right ) \log (3)+\left (-x+x^2+\left (-3 x^2+2 x^4\right ) \log (3)\right ) \log \left (x-x^2+\left (3 x^2-2 x^4\right ) \log (3)\right )\right ) \log \left (x^2-x \log \left (x-x^2+\left (3 x^2-2 x^4\right ) \log (3)\right )\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [F]
time = 2.68, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (2 x^{3}-3 x \right ) \ln \left (3\right )+x -1\right ) \ln \left (\left (-2 x^{4}+3 x^{2}\right ) \ln \left (3\right )-x^{2}+x \right )+\left (-4 x^{4}+8 x^{3}+6 x^{2}-6 x \right ) \ln \left (3\right )-2 x^{2}+4 x -1}{\left (\left (\left (2 x^{4}-3 x^{2}\right ) \ln \left (3\right )+x^{2}-x \right ) \ln \left (\left (-2 x^{4}+3 x^{2}\right ) \ln \left (3\right )-x^{2}+x \right )+\left (-2 x^{5}+3 x^{3}\right ) \ln \left (3\right )-x^{3}+x^{2}\right ) \ln \left (-x \ln \left (\left (-2 x^{4}+3 x^{2}\right ) \ln \left (3\right )-x^{2}+x \right )+x^{2}\right )}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.54, size = 31, normalized size = 1.00 \begin {gather*} \log \left (\log \left (x - \log \left (-2 \, x^{3} \log \left (3\right ) + x {\left (3 \, \log \left (3\right ) - 1\right )} + 1\right ) - \log \left (x\right )\right ) + \log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 32, normalized size = 1.03 \begin {gather*} \log \left (\log \left (x^{2} - x \log \left (-x^{2} - {\left (2 \, x^{4} - 3 \, x^{2}\right )} \log \left (3\right ) + x\right )\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 1.81, size = 27, normalized size = 0.87 \begin {gather*} \log {\left (\log {\left (x^{2} - x \log {\left (- x^{2} + x + \left (- 2 x^{4} + 3 x^{2}\right ) \log {\left (3 \right )} \right )} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.34, size = 31, normalized size = 1.00 \begin {gather*} \ln \left (\ln \left (x^2-x\,\ln \left (x+\ln \left (3\right )\,\left (3\,x^2-2\,x^4\right )-x^2\right )\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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