Optimal. Leaf size=27 \[ \left (-\frac {5}{3}+x-x^2\right ) \left (4+\frac {x^3}{2 \log \left (\log \left (x^2\right )\right )}\right ) \]
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Rubi [F] time = 0.76, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {10 x^2-6 x^3+6 x^4+\left (-15 x^2+12 x^3-15 x^4\right ) \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )+(24-48 x) \log \left (x^2\right ) \log ^2\left (\log \left (x^2\right )\right )}{6 \log \left (x^2\right ) \log ^2\left (\log \left (x^2\right )\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{6} \int \frac {10 x^2-6 x^3+6 x^4+\left (-15 x^2+12 x^3-15 x^4\right ) \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )+(24-48 x) \log \left (x^2\right ) \log ^2\left (\log \left (x^2\right )\right )}{\log \left (x^2\right ) \log ^2\left (\log \left (x^2\right )\right )} \, dx\\ &=\frac {1}{6} \int \left (-24 (-1+2 x)+\frac {2 x^2 \left (5-3 x+3 x^2\right )}{\log \left (x^2\right ) \log ^2\left (\log \left (x^2\right )\right )}-\frac {3 x^2 \left (5-4 x+5 x^2\right )}{\log \left (\log \left (x^2\right )\right )}\right ) \, dx\\ &=-(1-2 x)^2+\frac {1}{3} \int \frac {x^2 \left (5-3 x+3 x^2\right )}{\log \left (x^2\right ) \log ^2\left (\log \left (x^2\right )\right )} \, dx-\frac {1}{2} \int \frac {x^2 \left (5-4 x+5 x^2\right )}{\log \left (\log \left (x^2\right )\right )} \, dx\\ &=-(1-2 x)^2+\frac {1}{3} \int \left (\frac {5 x^2}{\log \left (x^2\right ) \log ^2\left (\log \left (x^2\right )\right )}-\frac {3 x^3}{\log \left (x^2\right ) \log ^2\left (\log \left (x^2\right )\right )}+\frac {3 x^4}{\log \left (x^2\right ) \log ^2\left (\log \left (x^2\right )\right )}\right ) \, dx-\frac {1}{2} \int \left (\frac {5 x^2}{\log \left (\log \left (x^2\right )\right )}-\frac {4 x^3}{\log \left (\log \left (x^2\right )\right )}+\frac {5 x^4}{\log \left (\log \left (x^2\right )\right )}\right ) \, dx\\ &=-(1-2 x)^2+\frac {5}{3} \int \frac {x^2}{\log \left (x^2\right ) \log ^2\left (\log \left (x^2\right )\right )} \, dx+2 \int \frac {x^3}{\log \left (\log \left (x^2\right )\right )} \, dx-\frac {5}{2} \int \frac {x^2}{\log \left (\log \left (x^2\right )\right )} \, dx-\frac {5}{2} \int \frac {x^4}{\log \left (\log \left (x^2\right )\right )} \, dx-\int \frac {x^3}{\log \left (x^2\right ) \log ^2\left (\log \left (x^2\right )\right )} \, dx+\int \frac {x^4}{\log \left (x^2\right ) \log ^2\left (\log \left (x^2\right )\right )} \, dx\\ &=-(1-2 x)^2-\frac {1}{2} \operatorname {Subst}\left (\int \frac {x}{\log (x) \log ^2(\log (x))} \, dx,x,x^2\right )+\frac {5}{3} \int \frac {x^2}{\log \left (x^2\right ) \log ^2\left (\log \left (x^2\right )\right )} \, dx-\frac {5}{2} \int \frac {x^2}{\log \left (\log \left (x^2\right )\right )} \, dx-\frac {5}{2} \int \frac {x^4}{\log \left (\log \left (x^2\right )\right )} \, dx+\int \frac {x^4}{\log \left (x^2\right ) \log ^2\left (\log \left (x^2\right )\right )} \, dx+\operatorname {Subst}\left (\int \frac {x}{\log (\log (x))} \, dx,x,x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.06, size = 33, normalized size = 1.22 \begin {gather*} 4 x-4 x^2-\frac {x^3 \left (5-3 x+3 x^2\right )}{6 \log \left (\log \left (x^2\right )\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.62, size = 39, normalized size = 1.44 \begin {gather*} -\frac {3 \, x^{5} - 3 \, x^{4} + 5 \, x^{3} + 24 \, {\left (x^{2} - x\right )} \log \left (\log \left (x^{2}\right )\right )}{6 \, \log \left (\log \left (x^{2}\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.32, size = 34, normalized size = 1.26 \begin {gather*} -4 \, x^{2} + 4 \, x - \frac {3 \, x^{5} - 3 \, x^{4} + 5 \, x^{3}}{6 \, \log \left (\log \left (x^{2}\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.02, size = 0, normalized size = 0.00 \[\int \frac {\left (-48 x +24\right ) \ln \left (x^{2}\right ) \ln \left (\ln \left (x^{2}\right )\right )^{2}+\left (-15 x^{4}+12 x^{3}-15 x^{2}\right ) \ln \left (x^{2}\right ) \ln \left (\ln \left (x^{2}\right )\right )+6 x^{4}-6 x^{3}+10 x^{2}}{6 \ln \left (x^{2}\right ) \ln \left (\ln \left (x^{2}\right )\right )^{2}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 35, normalized size = 1.30 \begin {gather*} -4 \, x^{2} + 4 \, x - \frac {3 \, x^{5} - 3 \, x^{4} + 5 \, x^{3}}{6 \, {\left (\log \relax (2) + \log \left (\log \relax (x)\right )\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.36, size = 80, normalized size = 2.96 \begin {gather*} 4\,x-\frac {\frac {x^3\,\left (3\,x^2-3\,x+5\right )}{6}-\frac {x^3\,\ln \left (x^2\right )\,\ln \left (\ln \left (x^2\right )\right )\,\left (5\,x^2-4\,x+5\right )}{4}}{\ln \left (\ln \left (x^2\right )\right )}-\ln \left (x^2\right )\,\left (\frac {5\,x^5}{4}-x^4+\frac {5\,x^3}{4}\right )-4\,x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.26, size = 31, normalized size = 1.15 \begin {gather*} - 4 x^{2} + 4 x + \frac {- 3 x^{5} + 3 x^{4} - 5 x^{3}}{6 \log {\left (\log {\left (x^{2} \right )} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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