Optimal. Leaf size=17 \[ 2 x^2 (1+\log (2)) (-4+2 \log (x))^4 \]
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Rubi [B] time = 0.10, antiderivative size = 60, normalized size of antiderivative = 3.53, number of steps used = 19, number of rules used = 4, integrand size = 55, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.073, Rules used = {6, 12, 2304, 2305} \begin {gather*} 32 x^2 (1+\log (2)) \log ^4(x)-256 x^2 (1+\log (2)) \log ^3(x)+768 x^2 (1+\log (2)) \log ^2(x)-1024 x^2 (1+\log (2)) \log (x)+512 x^2 (1+\log (2)) \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 2304
Rule 2305
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int (-512 x-512 x \log (2)) \log (x) \, dx+\int (768 x+768 x \log (2)) \log ^2(x) \, dx+\int (-384 x-384 x \log (2)) \log ^3(x) \, dx+\int (64 x+64 x \log (2)) \log ^4(x) \, dx\\ &=\int x (-512-512 \log (2)) \log (x) \, dx+\int x (768+768 \log (2)) \log ^2(x) \, dx+\int x (-384-384 \log (2)) \log ^3(x) \, dx+\int x (64+64 \log (2)) \log ^4(x) \, dx\\ &=(64 (1+\log (2))) \int x \log ^4(x) \, dx-(384 (1+\log (2))) \int x \log ^3(x) \, dx-(512 (1+\log (2))) \int x \log (x) \, dx+(768 (1+\log (2))) \int x \log ^2(x) \, dx\\ &=128 x^2 (1+\log (2))-256 x^2 (1+\log (2)) \log (x)+384 x^2 (1+\log (2)) \log ^2(x)-192 x^2 (1+\log (2)) \log ^3(x)+32 x^2 (1+\log (2)) \log ^4(x)-(128 (1+\log (2))) \int x \log ^3(x) \, dx+(576 (1+\log (2))) \int x \log ^2(x) \, dx-(768 (1+\log (2))) \int x \log (x) \, dx\\ &=320 x^2 (1+\log (2))-640 x^2 (1+\log (2)) \log (x)+672 x^2 (1+\log (2)) \log ^2(x)-256 x^2 (1+\log (2)) \log ^3(x)+32 x^2 (1+\log (2)) \log ^4(x)+(192 (1+\log (2))) \int x \log ^2(x) \, dx-(576 (1+\log (2))) \int x \log (x) \, dx\\ &=464 x^2 (1+\log (2))-928 x^2 (1+\log (2)) \log (x)+768 x^2 (1+\log (2)) \log ^2(x)-256 x^2 (1+\log (2)) \log ^3(x)+32 x^2 (1+\log (2)) \log ^4(x)-(192 (1+\log (2))) \int x \log (x) \, dx\\ &=512 x^2 (1+\log (2))-1024 x^2 (1+\log (2)) \log (x)+768 x^2 (1+\log (2)) \log ^2(x)-256 x^2 (1+\log (2)) \log ^3(x)+32 x^2 (1+\log (2)) \log ^4(x)\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.02, size = 48, normalized size = 2.82 \begin {gather*} 64 (1+\log (2)) \left (8 x^2-16 x^2 \log (x)+12 x^2 \log ^2(x)-4 x^2 \log ^3(x)+\frac {1}{2} x^2 \log ^4(x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.65, size = 75, normalized size = 4.41 \begin {gather*} 32 \, {\left (x^{2} \log \relax (2) + x^{2}\right )} \log \relax (x)^{4} - 256 \, {\left (x^{2} \log \relax (2) + x^{2}\right )} \log \relax (x)^{3} + 512 \, x^{2} \log \relax (2) + 768 \, {\left (x^{2} \log \relax (2) + x^{2}\right )} \log \relax (x)^{2} + 512 \, x^{2} - 1024 \, {\left (x^{2} \log \relax (2) + x^{2}\right )} \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.16, size = 89, normalized size = 5.24 \begin {gather*} 32 \, x^{2} \log \relax (2) \log \relax (x)^{4} - 256 \, x^{2} \log \relax (2) \log \relax (x)^{3} + 32 \, x^{2} \log \relax (x)^{4} + 768 \, x^{2} \log \relax (2) \log \relax (x)^{2} - 256 \, x^{2} \log \relax (x)^{3} - 1024 \, x^{2} \log \relax (2) \log \relax (x) + 768 \, x^{2} \log \relax (x)^{2} + 512 \, x^{2} \log \relax (2) - 1024 \, x^{2} \log \relax (x) + 512 \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.04, size = 64, normalized size = 3.76
method | result | size |
risch | \(32 x^{2} \left (1+\ln \relax (2)\right ) \ln \relax (x )^{4}-256 x^{2} \left (1+\ln \relax (2)\right ) \ln \relax (x )^{3}+768 x^{2} \left (1+\ln \relax (2)\right ) \ln \relax (x )^{2}-1024 x^{2} \left (1+\ln \relax (2)\right ) \ln \relax (x )+512 x^{2} \ln \relax (2)+512 x^{2}\) | \(64\) |
norman | \(\left (512 \ln \relax (2)+512\right ) x^{2}+\left (-1024-1024 \ln \relax (2)\right ) x^{2} \ln \relax (x )+\left (-256 \ln \relax (2)-256\right ) x^{2} \ln \relax (x )^{3}+\left (32 \ln \relax (2)+32\right ) x^{2} \ln \relax (x )^{4}+\left (768 \ln \relax (2)+768\right ) x^{2} \ln \relax (x )^{2}\) | \(66\) |
default | \(-1024 x^{2} \ln \relax (x )+512 x^{2}-1024 x^{2} \ln \relax (2) \ln \relax (x )+512 x^{2} \ln \relax (2)-256 x^{2} \ln \relax (x )^{3}+768 x^{2} \ln \relax (x )^{2}-256 \ln \relax (2) x^{2} \ln \relax (x )^{3}+768 x^{2} \ln \relax (2) \ln \relax (x )^{2}+32 x^{2} \ln \relax (x )^{4}+32 \ln \relax (2) x^{2} \ln \relax (x )^{4}\) | \(90\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.43, size = 139, normalized size = 8.18 \begin {gather*} 16 \, {\left (2 \, {\left (\log \relax (2) + 1\right )} \log \relax (x)^{4} - 4 \, {\left (\log \relax (2) + 1\right )} \log \relax (x)^{3} + 6 \, {\left (\log \relax (2) + 1\right )} \log \relax (x)^{2} - 6 \, {\left (\log \relax (2) + 1\right )} \log \relax (x) + 3 \, \log \relax (2) + 3\right )} x^{2} - 48 \, {\left (4 \, {\left (\log \relax (2) + 1\right )} \log \relax (x)^{3} - 6 \, {\left (\log \relax (2) + 1\right )} \log \relax (x)^{2} + 6 \, {\left (\log \relax (2) + 1\right )} \log \relax (x) - 3 \, \log \relax (2) - 3\right )} x^{2} + 192 \, {\left (2 \, {\left (\log \relax (2) + 1\right )} \log \relax (x)^{2} - 2 \, {\left (\log \relax (2) + 1\right )} \log \relax (x) + \log \relax (2) + 1\right )} x^{2} + 128 \, x^{2} {\left (\log \relax (2) + 1\right )} - 256 \, {\left (x^{2} \log \relax (2) + x^{2}\right )} \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.24, size = 15, normalized size = 0.88 \begin {gather*} 32\,x^2\,{\left (\ln \relax (x)-2\right )}^4\,\left (\ln \relax (2)+1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.29, size = 85, normalized size = 5.00 \begin {gather*} x^{2} \left (512 \log {\relax (2 )} + 512\right ) + \left (- 1024 x^{2} - 1024 x^{2} \log {\relax (2 )}\right ) \log {\relax (x )} + \left (- 256 x^{2} - 256 x^{2} \log {\relax (2 )}\right ) \log {\relax (x )}^{3} + \left (32 x^{2} \log {\relax (2 )} + 32 x^{2}\right ) \log {\relax (x )}^{4} + \left (768 x^{2} \log {\relax (2 )} + 768 x^{2}\right ) \log {\relax (x )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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