Optimal. Leaf size=24 \[ 5-x-4 x^4 \log ^4(x) \log ^2\left (\frac {3 \log (2)}{e^2}\right ) \]
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Rubi [A] time = 0.10, antiderivative size = 22, normalized size of antiderivative = 0.92, number of steps used = 9, number of rules used = 2, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {2305, 2304} \begin {gather*} -4 x^4 (2-\log (\log (8)))^2 \log ^4(x)-x \end {gather*}
Antiderivative was successfully verified.
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Rule 2304
Rule 2305
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-x+\log ^2\left (\frac {3 \log (2)}{e^2}\right ) \int \left (-16 x^3 \log ^3(x)-16 x^3 \log ^4(x)\right ) \, dx\\ &=-x-\left (16 (2-\log (\log (8)))^2\right ) \int x^3 \log ^3(x) \, dx-\left (16 (2-\log (\log (8)))^2\right ) \int x^3 \log ^4(x) \, dx\\ &=-x-4 x^4 \log ^3(x) (2-\log (\log (8)))^2-4 x^4 \log ^4(x) (2-\log (\log (8)))^2+\left (12 (2-\log (\log (8)))^2\right ) \int x^3 \log ^2(x) \, dx+\left (16 (2-\log (\log (8)))^2\right ) \int x^3 \log ^3(x) \, dx\\ &=-x+3 x^4 \log ^2(x) (2-\log (\log (8)))^2-4 x^4 \log ^4(x) (2-\log (\log (8)))^2-\left (6 (2-\log (\log (8)))^2\right ) \int x^3 \log (x) \, dx-\left (12 (2-\log (\log (8)))^2\right ) \int x^3 \log ^2(x) \, dx\\ &=-x+\frac {3}{8} x^4 (2-\log (\log (8)))^2-\frac {3}{2} x^4 \log (x) (2-\log (\log (8)))^2-4 x^4 \log ^4(x) (2-\log (\log (8)))^2+\left (6 (2-\log (\log (8)))^2\right ) \int x^3 \log (x) \, dx\\ &=-x-4 x^4 \log ^4(x) (2-\log (\log (8)))^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 20, normalized size = 0.83 \begin {gather*} -x-4 x^4 \log ^4(x) (-2+\log (\log (8)))^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.75, size = 22, normalized size = 0.92 \begin {gather*} -4 \, x^{4} \log \left (3 \, e^{\left (-2\right )} \log \relax (2)\right )^{2} \log \relax (x)^{4} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 22, normalized size = 0.92 \begin {gather*} -4 \, x^{4} \log \left (3 \, e^{\left (-2\right )} \log \relax (2)\right )^{2} \log \relax (x)^{4} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 23, normalized size = 0.96
method | result | size |
risch | \(-4 \left (\ln \relax (3)+\ln \left (\ln \relax (2)\right )-2\right )^{2} x^{4} \ln \relax (x )^{4}-x\) | \(23\) |
default | \(-x -4 \ln \relax (x )^{4} x^{4} \ln \left (3 \ln \relax (2) {\mathrm e}^{-2}\right )^{2}\) | \(25\) |
norman | \(\left (-4 \ln \relax (3)^{2}-8 \ln \relax (3) \ln \left (\ln \relax (2)\right )-4 \ln \left (\ln \relax (2)\right )^{2}+16 \ln \relax (3)+16 \ln \left (\ln \relax (2)\right )-16\right ) x^{4} \ln \relax (x )^{4}-x\) | \(44\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.40, size = 66, normalized size = 2.75 \begin {gather*} -\frac {1}{8} \, {\left ({\left (32 \, \log \relax (x)^{4} - 32 \, \log \relax (x)^{3} + 24 \, \log \relax (x)^{2} - 12 \, \log \relax (x) + 3\right )} x^{4} + {\left (32 \, \log \relax (x)^{3} - 24 \, \log \relax (x)^{2} + 12 \, \log \relax (x) - 3\right )} x^{4}\right )} \log \left (3 \, e^{\left (-2\right )} \log \relax (2)\right )^{2} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.41, size = 22, normalized size = 0.92 \begin {gather*} -4\,{\ln \left (3\,{\mathrm {e}}^{-2}\,\ln \relax (2)\right )}^2\,x^4\,{\ln \relax (x)}^4-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.17, size = 65, normalized size = 2.71 \begin {gather*} - x + \left (- 16 x^{4} + 16 x^{4} \log {\left (\log {\relax (2 )} \right )} - 4 x^{4} \log {\relax (3 )}^{2} - 4 x^{4} \log {\left (\log {\relax (2 )} \right )}^{2} - 8 x^{4} \log {\relax (3 )} \log {\left (\log {\relax (2 )} \right )} + 16 x^{4} \log {\relax (3 )}\right ) \log {\relax (x )}^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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