Optimal. Leaf size=18 \[ \left (6-2 x^3 (2-x+\log (\log (\log (x))))\right )^2 \]
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Rubi [A] time = 0.27, antiderivative size = 23, normalized size of antiderivative = 1.28, number of steps used = 3, number of rules used = 3, integrand size = 107, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.028, Rules used = {6688, 12, 6686} \begin {gather*} 4 \left (x^4-2 x^3-x^3 \log (\log (\log (x)))+3\right )^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6686
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {8 x^2 (1-\log (x) \log (\log (x)) (-6+4 x-3 \log (\log (\log (x))))) \left (-3+2 x^3-x^4+x^3 \log (\log (\log (x)))\right )}{\log (x) \log (\log (x))} \, dx\\ &=8 \int \frac {x^2 (1-\log (x) \log (\log (x)) (-6+4 x-3 \log (\log (\log (x))))) \left (-3+2 x^3-x^4+x^3 \log (\log (\log (x)))\right )}{\log (x) \log (\log (x))} \, dx\\ &=4 \left (3-2 x^3+x^4-x^3 \log (\log (\log (x)))\right )^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 23, normalized size = 1.28 \begin {gather*} 4 \left (3-2 x^3+x^4-x^3 \log (\log (\log (x)))\right )^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.67, size = 57, normalized size = 3.17 \begin {gather*} 4 \, x^{8} + 4 \, x^{6} \log \left (\log \left (\log \relax (x)\right )\right )^{2} - 16 \, x^{7} + 16 \, x^{6} + 24 \, x^{4} - 48 \, x^{3} - 8 \, {\left (x^{7} - 2 \, x^{6} + 3 \, x^{3}\right )} \log \left (\log \left (\log \relax (x)\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.31, size = 122, normalized size = 6.78 \begin {gather*} 2 \, x^{6} \log \relax (x)^{2} \log \left (\log \relax (x)\right )^{2} - 8 \, x^{7} \log \relax (x) \log \left (\log \relax (x)\right ) + 4 \, x^{6} \log \relax (x) \log \left (\log \relax (x)\right ) \log \left (\log \left (\log \relax (x)\right )\right ) + 4 \, x^{8} + 8 \, x^{6} \log \relax (x) \log \left (\log \relax (x)\right ) - 8 \, x^{7} \log \left (\log \left (\log \relax (x)\right )\right ) + 4 \, x^{6} \log \left (\log \left (\log \relax (x)\right )\right )^{2} - 16 \, x^{7} + 16 \, x^{6} \log \left (\log \left (\log \relax (x)\right )\right ) + \frac {46}{3} \, x^{6} - 24 \, x^{3} \log \relax (x) \log \left (\log \relax (x)\right ) + 24 \, x^{4} - 24 \, x^{3} \log \left (\log \left (\log \relax (x)\right )\right ) - 48 \, x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.04, size = 59, normalized size = 3.28
method | result | size |
risch | \(4 x^{6} \ln \left (\ln \left (\ln \relax (x )\right )\right )^{2}+\left (-8 x^{7}+16 x^{6}-24 x^{3}\right ) \ln \left (\ln \left (\ln \relax (x )\right )\right )+4 x^{8}-16 x^{7}+16 x^{6}+24 x^{4}-48 x^{3}\) | \(59\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.44, size = 57, normalized size = 3.17 \begin {gather*} 4 \, x^{8} + 4 \, x^{6} \log \left (\log \left (\log \relax (x)\right )\right )^{2} - 16 \, x^{7} + 16 \, x^{6} + 24 \, x^{4} - 48 \, x^{3} - 8 \, {\left (x^{7} - 2 \, x^{6} + 3 \, x^{3}\right )} \log \left (\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 = 3.86, size = 62, normalized size = 3.44 \begin {gather*} 4\,x^6\,{\ln \left (\ln \left (\ln \relax (x)\right )\right )}^2-48\,x^3+24\,x^4+16\,x^6-16\,x^7+4\,x^8-\frac {\ln \left (\ln \left (\ln \relax (x)\right )\right )\,\left (8\,x^8-16\,x^7+24\,x^4\right )}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.93, size = 60, normalized size = 3.33 \begin {gather*} 4 x^{8} - 16 x^{7} + 4 x^{6} \log {\left (\log {\left (\log {\relax (x )} \right )} \right )}^{2} + 16 x^{6} + 24 x^{4} - 48 x^{3} + \left (- 8 x^{7} + 16 x^{6} - 24 x^{3}\right ) \log {\left (\log {\left (\log {\relax (x )} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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