Optimal. Leaf size=27 \[ \log \left (\log ^2\left (e^{\frac {1}{\log \left (x+\frac {1}{4} (1-2 x)^2 x^2\right )}} x\right )\right ) \]
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Rubi [A] time = 0.16, antiderivative size = 32, normalized size of antiderivative = 1.19, number of steps used = 1, number of rules used = 1, integrand size = 130, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.008, Rules used = {6684} \begin {gather*} 2 \log \left (\log \left (x e^{\frac {1}{\log \left (\frac {1}{4} \left (4 x^4-4 x^3+x^2+4 x\right )\right )}}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6684
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=2 \log \left (\log \left (e^{\frac {1}{\log \left (\frac {1}{4} \left (4 x+x^2-4 x^3+4 x^4\right )\right )}} x\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.06, size = 28, normalized size = 1.04 \begin {gather*} 2 \log \left (\log \left (e^{\frac {1}{\log \left (x+\frac {x^2}{4}-x^3+x^4\right )}} x\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.55, size = 25, normalized size = 0.93 \begin {gather*} 2 \, \log \left (\log \left (x e^{\left (\frac {1}{\log \left (x^{4} - x^{3} + \frac {1}{4} \, x^{2} + x\right )}\right )}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 23.29, size = 64, normalized size = 2.37 \begin {gather*} 2 \, \log \left (2 \, \log \relax (2) \log \relax (x) - \log \left (4 \, x^{3} - 4 \, x^{2} + x + 4\right ) \log \relax (x) - \log \relax (x)^{2} - 1\right ) - 2 \, \log \left (2 \, \log \relax (2) - \log \left (4 \, x^{3} - 4 \, x^{2} + x + 4\right ) - \log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.14, size = 0, normalized size = 0.00 \[\int \frac {\left (8 x^{3}-8 x^{2}+2 x +8\right ) \ln \left (x^{4}-x^{3}+\frac {1}{4} x^{2}+x \right )^{2}-32 x^{3}+24 x^{2}-4 x -8}{\left (4 x^{4}-4 x^{3}+x^{2}+4 x \right ) \ln \left (x^{4}-x^{3}+\frac {1}{4} x^{2}+x \right )^{2} \ln \left (x \,{\mathrm e}^{\frac {1}{\ln \left (x^{4}-x^{3}+\frac {1}{4} x^{2}+x \right )}}\right )}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.54, size = 37, normalized size = 1.37 \begin {gather*} 2 \, \log \left (\log \relax (x) + \log \left (e^{\left (-\frac {1}{2 \, \log \relax (2) - \log \left (4 \, x^{3} - 4 \, x^{2} + x + 4\right ) - \log \relax (x)}\right )}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 6.87, size = 25, normalized size = 0.93 \begin {gather*} 2\,\ln \left (\ln \left (x\,{\mathrm {e}}^{\frac {1}{\ln \left (x^4-x^3+\frac {x^2}{4}+x\right )}}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.62, size = 24, normalized size = 0.89 \begin {gather*} 2 \log {\left (\log {\left (x e^{\frac {1}{\log {\left (x^{4} - x^{3} + \frac {x^{2}}{4} + x \right )}}} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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