Optimal. Leaf size=24 \[ 2 x \left (x-16 \left (\frac {x}{3}+4 (3+x)-\log (2)\right )^2\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 35, normalized size of antiderivative = 1.46, number of steps used = 2, number of rules used = 1, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.036, Rules used = {12} \begin {gather*} -\frac {5408 x^3}{9}-3326 x^2-32 x \left (144+\log ^2(2)\right )+\frac {64}{39} (13 x+18)^2 \log (2) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int \left (-13824-19956 x-5408 x^2+(2304+1664 x) \log (2)-96 \log ^2(2)\right ) \, dx\\ &=-3326 x^2-\frac {5408 x^3}{9}+\frac {64}{39} (18+13 x)^2 \log (2)-32 x \left (144+\log ^2(2)\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 35, normalized size = 1.46 \begin {gather*} -\frac {4}{3} \left (\frac {4989 x^2}{2}+\frac {1352 x^3}{3}+24 x (-12+\log (2))^2-208 x^2 \log (2)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 34, normalized size = 1.42 \begin {gather*} -\frac {5408}{9} \, x^{3} - 32 \, x \log \relax (2)^{2} - 3326 \, x^{2} + \frac {64}{3} \, {\left (13 \, x^{2} + 36 \, x\right )} \log \relax (2) - 4608 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 34, normalized size = 1.42 \begin {gather*} -\frac {5408}{9} \, x^{3} - 32 \, x \log \relax (2)^{2} - 3326 \, x^{2} + \frac {64}{3} \, {\left (13 \, x^{2} + 36 \, x\right )} \log \relax (2) - 4608 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 29, normalized size = 1.21
method | result | size |
gosper | \(-\frac {2 x \left (144 \ln \relax (2)^{2}-1248 x \ln \relax (2)+2704 x^{2}-3456 \ln \relax (2)+14967 x +20736\right )}{9}\) | \(29\) |
norman | \(\left (\frac {832 \ln \relax (2)}{3}-3326\right ) x^{2}+\left (-32 \ln \relax (2)^{2}+768 \ln \relax (2)-4608\right ) x -\frac {5408 x^{3}}{9}\) | \(31\) |
risch | \(-32 x \ln \relax (2)^{2}+\frac {832 x^{2} \ln \relax (2)}{3}+768 x \ln \relax (2)-\frac {5408 x^{3}}{9}-3326 x^{2}-4608 x\) | \(34\) |
default | \(-32 x \ln \relax (2)^{2}+\frac {\ln \relax (2) \left (832 x^{2}+2304 x \right )}{3}-\frac {5408 x^{3}}{9}-3326 x^{2}-4608 x\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 34, normalized size = 1.42 \begin {gather*} -\frac {5408}{9} \, x^{3} - 32 \, x \log \relax (2)^{2} - 3326 \, x^{2} + \frac {64}{3} \, {\left (13 \, x^{2} + 36 \, x\right )} \log \relax (2) - 4608 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.09, size = 31, normalized size = 1.29 \begin {gather*} -\frac {5408\,x^3}{9}+\left (\frac {832\,\ln \relax (2)}{3}-3326\right )\,x^2+\left (768\,\ln \relax (2)-32\,{\ln \relax (2)}^2-4608\right )\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 32, normalized size = 1.33 \begin {gather*} - \frac {5408 x^{3}}{9} + x^{2} \left (-3326 + \frac {832 \log {\relax (2 )}}{3}\right ) + x \left (-4608 - 32 \log {\relax (2 )}^{2} + 768 \log {\relax (2 )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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