Optimal. Leaf size=32 \[ -\frac {-4-e^3}{2 x}+x-\log ^4\left (\frac {1}{16} x^4 \log ^2(x)\right ) \]
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Rubi [A] time = 0.26, antiderivative size = 30, normalized size of antiderivative = 0.94, number of steps used = 6, number of rules used = 4, integrand size = 51, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.078, Rules used = {12, 6742, 14, 6686} \begin {gather*} -\log ^4\left (\frac {1}{16} x^4 \log ^2(x)\right )+x+\frac {4+e^3}{2 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 6686
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \frac {\left (-4-e^3+2 x^2\right ) \log (x)+(-16 x-32 x \log (x)) \log ^3\left (\frac {1}{16} x^4 \log ^2(x)\right )}{x^2 \log (x)} \, dx\\ &=\frac {1}{2} \int \left (\frac {-4-e^3+2 x^2}{x^2}-\frac {16 (1+2 \log (x)) \log ^3\left (\frac {1}{16} x^4 \log ^2(x)\right )}{x \log (x)}\right ) \, dx\\ &=\frac {1}{2} \int \frac {-4-e^3+2 x^2}{x^2} \, dx-8 \int \frac {(1+2 \log (x)) \log ^3\left (\frac {1}{16} x^4 \log ^2(x)\right )}{x \log (x)} \, dx\\ &=-\log ^4\left (\frac {1}{16} x^4 \log ^2(x)\right )+\frac {1}{2} \int \left (2+\frac {-4-e^3}{x^2}\right ) \, dx\\ &=\frac {4+e^3}{2 x}+x-\log ^4\left (\frac {1}{16} x^4 \log ^2(x)\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.07, size = 33, normalized size = 1.03 \begin {gather*} \frac {2}{x}+\frac {e^3}{2 x}+x-\log ^4\left (\frac {1}{16} x^4 \log ^2(x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.00, size = 31, normalized size = 0.97 \begin {gather*} -\frac {2 \, x \log \left (\frac {1}{16} \, x^{4} \log \relax (x)^{2}\right )^{4} - 2 \, x^{2} - e^{3} - 4}{2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.84, size = 178, normalized size = 5.56 \begin {gather*} -\frac {1536 \, x \log \relax (2)^{2} \log \relax (x) \log \left (\log \relax (x)^{2}\right ) - 1536 \, x \log \relax (2) \log \relax (x)^{2} \log \left (\log \relax (x)^{2}\right ) + 512 \, x \log \relax (x)^{3} \log \left (\log \relax (x)^{2}\right ) + 192 \, x \log \relax (2)^{2} \log \left (\log \relax (x)^{2}\right )^{2} - 384 \, x \log \relax (2) \log \relax (x) \log \left (\log \relax (x)^{2}\right )^{2} + 192 \, x \log \relax (x)^{2} \log \left (\log \relax (x)^{2}\right )^{2} - 32 \, x \log \relax (2) \log \left (\log \relax (x)^{2}\right )^{3} + 32 \, x \log \relax (x) \log \left (\log \relax (x)^{2}\right )^{3} + 2 \, x \log \left (\log \relax (x)^{2}\right )^{4} - 2048 \, x \log \relax (2)^{3} \log \relax (x) + 3072 \, x \log \relax (2)^{2} \log \relax (x)^{2} - 2048 \, x \log \relax (2) \log \relax (x)^{3} + 512 \, x \log \relax (x)^{4} - 1024 \, x \log \relax (2)^{3} \log \left (\log \relax (x)\right ) - 2 \, x^{2} - e^{3} - 4}{2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 19.13, size = 106036, normalized size = 3313.62
method | result | size |
risch | \(\text {Expression too large to display}\) | \(106036\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.43, size = 188, normalized size = 5.88 \begin {gather*} -16 \, \log \left (\frac {1}{16} \, x^{4} \log \relax (x)^{2}\right )^{3} \log \relax (x) + 256 \, \log \relax (x)^{4} + 128 \, \log \relax (2) \log \left (\log \relax (x)\right )^{3} - 16 \, \log \left (\log \relax (x)\right )^{4} + 96 \, {\left (\log \relax (x)^{2} + \log \relax (x)\right )} \log \left (\frac {1}{16} \, x^{4} \log \relax (x)^{2}\right )^{2} + 192 \, {\left (4 \, \log \relax (2) + 1\right )} \log \relax (x)^{2} + 768 \, \log \relax (x)^{3} - 384 \, {\left (\log \relax (2)^{2} + \log \relax (x)\right )} \log \left (\log \relax (x)\right )^{2} - 64 \, {\left (4 \, \log \relax (x)^{3} + 9 \, \log \relax (x)^{2} + 6 \, \log \relax (x)\right )} \log \left (\frac {1}{16} \, x^{4} \log \relax (x)^{2}\right ) - 768 \, {\left (2 \, \log \relax (2)^{2} + 2 \, \log \relax (2) + 1\right )} \log \relax (x) + 1344 \, \log \relax (x)^{2} + 128 \, {\left (4 \, \log \relax (2)^{3} + 6 \, {\left (2 \, \log \relax (2) + 1\right )} \log \relax (x) - 3 \, \log \relax (x)^{2}\right )} \log \left (\log \relax (x)\right ) + x + \frac {e^{3}}{2 \, x} + \frac {2}{x} + 768 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.81, size = 26, normalized size = 0.81 \begin {gather*} x-{\ln \left (\frac {x^4\,{\ln \relax (x)}^2}{16}\right )}^4+\frac {\frac {{\mathrm {e}}^3}{2}+2}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.32, size = 22, normalized size = 0.69 \begin {gather*} x - \log {\left (\frac {x^{4} \log {\relax (x )}^{2}}{16} \right )}^{4} + \frac {4 + e^{3}}{2 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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