Optimal. Leaf size=32 \[ \log \left (5 e^{-x} x \log \left (1+3 \left (x+\frac {2-x+x^2-\log (x)}{x}\right )\right )\right ) \]
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Rubi [F] time = 2.20, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {9-6 x^2-3 \log (x)+\left (-6+8 x-8 x^2+6 x^3+(3-3 x) \log (x)\right ) \log \left (\frac {6-2 x+6 x^2-3 \log (x)}{x}\right )}{\left (-6 x+2 x^2-6 x^3+3 x \log (x)\right ) \log \left (\frac {6-2 x+6 x^2-3 \log (x)}{x}\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-9+6 x^2+3 \log (x)-\left (-6+8 x-8 x^2+6 x^3+(3-3 x) \log (x)\right ) \log \left (\frac {6-2 x+6 x^2-3 \log (x)}{x}\right )}{\left (6 x-2 x^2+6 x^3-3 x \log (x)\right ) \log \left (-2+\frac {6}{x}+6 x-\frac {3 \log (x)}{x}\right )} \, dx\\ &=\int \left (-\frac {8}{6-2 x+6 x^2-3 \log (x)}+\frac {6}{x \left (6-2 x+6 x^2-3 \log (x)\right )}+\frac {8 x}{6-2 x+6 x^2-3 \log (x)}-\frac {6 x^2}{6-2 x+6 x^2-3 \log (x)}+\frac {3 \log (x)}{6-2 x+6 x^2-3 \log (x)}-\frac {3 \log (x)}{x \left (6-2 x+6 x^2-3 \log (x)\right )}+\frac {6 x}{\left (6-2 x+6 x^2-3 \log (x)\right ) \log \left (-2+\frac {6}{x}+6 x-\frac {3 \log (x)}{x}\right )}+\frac {3 \log (x)}{x \left (6-2 x+6 x^2-3 \log (x)\right ) \log \left (-2+\frac {6}{x}+6 x-\frac {3 \log (x)}{x}\right )}+\frac {9}{x \left (-6+2 x-6 x^2+3 \log (x)\right ) \log \left (-2+\frac {6}{x}+6 x-\frac {3 \log (x)}{x}\right )}\right ) \, dx\\ &=3 \int \frac {\log (x)}{6-2 x+6 x^2-3 \log (x)} \, dx-3 \int \frac {\log (x)}{x \left (6-2 x+6 x^2-3 \log (x)\right )} \, dx+3 \int \frac {\log (x)}{x \left (6-2 x+6 x^2-3 \log (x)\right ) \log \left (-2+\frac {6}{x}+6 x-\frac {3 \log (x)}{x}\right )} \, dx+6 \int \frac {1}{x \left (6-2 x+6 x^2-3 \log (x)\right )} \, dx-6 \int \frac {x^2}{6-2 x+6 x^2-3 \log (x)} \, dx+6 \int \frac {x}{\left (6-2 x+6 x^2-3 \log (x)\right ) \log \left (-2+\frac {6}{x}+6 x-\frac {3 \log (x)}{x}\right )} \, dx-8 \int \frac {1}{6-2 x+6 x^2-3 \log (x)} \, dx+8 \int \frac {x}{6-2 x+6 x^2-3 \log (x)} \, dx+9 \int \frac {1}{x \left (-6+2 x-6 x^2+3 \log (x)\right ) \log \left (-2+\frac {6}{x}+6 x-\frac {3 \log (x)}{x}\right )} \, dx\\ &=3 \int \left (-\frac {1}{3}+\frac {2 \left (3-x+3 x^2\right )}{3 \left (6-2 x+6 x^2-3 \log (x)\right )}\right ) \, dx-3 \int \left (-\frac {1}{3 x}+\frac {2 \left (3-x+3 x^2\right )}{3 x \left (6-2 x+6 x^2-3 \log (x)\right )}\right ) \, dx+3 \int \frac {\log (x)}{x \left (6-2 x+6 x^2-3 \log (x)\right ) \log \left (-2+\frac {6}{x}+6 x-\frac {3 \log (x)}{x}\right )} \, dx+6 \int \frac {1}{x \left (6-2 x+6 x^2-3 \log (x)\right )} \, dx-6 \int \frac {x^2}{6-2 x+6 x^2-3 \log (x)} \, dx+6 \int \frac {x}{\left (6-2 x+6 x^2-3 \log (x)\right ) \log \left (-2+\frac {6}{x}+6 x-\frac {3 \log (x)}{x}\right )} \, dx-8 \int \frac {1}{6-2 x+6 x^2-3 \log (x)} \, dx+8 \int \frac {x}{6-2 x+6 x^2-3 \log (x)} \, dx+9 \int \frac {1}{x \left (-6+2 x-6 x^2+3 \log (x)\right ) \log \left (-2+\frac {6}{x}+6 x-\frac {3 \log (x)}{x}\right )} \, dx\\ &=-x+\log (x)+2 \int \frac {3-x+3 x^2}{6-2 x+6 x^2-3 \log (x)} \, dx-2 \int \frac {3-x+3 x^2}{x \left (6-2 x+6 x^2-3 \log (x)\right )} \, dx+3 \int \frac {\log (x)}{x \left (6-2 x+6 x^2-3 \log (x)\right ) \log \left (-2+\frac {6}{x}+6 x-\frac {3 \log (x)}{x}\right )} \, dx+6 \int \frac {1}{x \left (6-2 x+6 x^2-3 \log (x)\right )} \, dx-6 \int \frac {x^2}{6-2 x+6 x^2-3 \log (x)} \, dx+6 \int \frac {x}{\left (6-2 x+6 x^2-3 \log (x)\right ) \log \left (-2+\frac {6}{x}+6 x-\frac {3 \log (x)}{x}\right )} \, dx-8 \int \frac {1}{6-2 x+6 x^2-3 \log (x)} \, dx+8 \int \frac {x}{6-2 x+6 x^2-3 \log (x)} \, dx+9 \int \frac {1}{x \left (-6+2 x-6 x^2+3 \log (x)\right ) \log \left (-2+\frac {6}{x}+6 x-\frac {3 \log (x)}{x}\right )} \, dx\\ &=-x+\log (x)+2 \int \left (\frac {3}{6-2 x+6 x^2-3 \log (x)}-\frac {x}{6-2 x+6 x^2-3 \log (x)}+\frac {3 x^2}{6-2 x+6 x^2-3 \log (x)}\right ) \, dx-2 \int \left (\frac {3}{x \left (6-2 x+6 x^2-3 \log (x)\right )}+\frac {3 x}{6-2 x+6 x^2-3 \log (x)}+\frac {1}{-6+2 x-6 x^2+3 \log (x)}\right ) \, dx+3 \int \frac {\log (x)}{x \left (6-2 x+6 x^2-3 \log (x)\right ) \log \left (-2+\frac {6}{x}+6 x-\frac {3 \log (x)}{x}\right )} \, dx+6 \int \frac {1}{x \left (6-2 x+6 x^2-3 \log (x)\right )} \, dx-6 \int \frac {x^2}{6-2 x+6 x^2-3 \log (x)} \, dx+6 \int \frac {x}{\left (6-2 x+6 x^2-3 \log (x)\right ) \log \left (-2+\frac {6}{x}+6 x-\frac {3 \log (x)}{x}\right )} \, dx-8 \int \frac {1}{6-2 x+6 x^2-3 \log (x)} \, dx+8 \int \frac {x}{6-2 x+6 x^2-3 \log (x)} \, dx+9 \int \frac {1}{x \left (-6+2 x-6 x^2+3 \log (x)\right ) \log \left (-2+\frac {6}{x}+6 x-\frac {3 \log (x)}{x}\right )} \, dx\\ &=-x+\log (x)-2 \int \frac {x}{6-2 x+6 x^2-3 \log (x)} \, dx-2 \int \frac {1}{-6+2 x-6 x^2+3 \log (x)} \, dx+3 \int \frac {\log (x)}{x \left (6-2 x+6 x^2-3 \log (x)\right ) \log \left (-2+\frac {6}{x}+6 x-\frac {3 \log (x)}{x}\right )} \, dx+6 \int \frac {1}{6-2 x+6 x^2-3 \log (x)} \, dx-6 \int \frac {x}{6-2 x+6 x^2-3 \log (x)} \, dx+6 \int \frac {x}{\left (6-2 x+6 x^2-3 \log (x)\right ) \log \left (-2+\frac {6}{x}+6 x-\frac {3 \log (x)}{x}\right )} \, dx-8 \int \frac {1}{6-2 x+6 x^2-3 \log (x)} \, dx+8 \int \frac {x}{6-2 x+6 x^2-3 \log (x)} \, dx+9 \int \frac {1}{x \left (-6+2 x-6 x^2+3 \log (x)\right ) \log \left (-2+\frac {6}{x}+6 x-\frac {3 \log (x)}{x}\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.05, size = 26, normalized size = 0.81 \begin {gather*} -x+\log (x)+\log \left (\log \left (\frac {6-2 x+6 x^2-3 \log (x)}{x}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 26, normalized size = 0.81 \begin {gather*} -x + \log \relax (x) + \log \left (\log \left (\frac {6 \, x^{2} - 2 \, x - 3 \, \log \relax (x) + 6}{x}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 27, normalized size = 0.84 \begin {gather*} -x + \log \relax (x) + \log \left (\log \left (6 \, x^{2} - 2 \, x - 3 \, \log \relax (x) + 6\right ) - \log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.17, size = 27, normalized size = 0.84
method | result | size |
norman | \(-x +\ln \relax (x )+\ln \left (\ln \left (\frac {-3 \ln \relax (x )+6 x^{2}-2 x +6}{x}\right )\right )\) | \(27\) |
risch | \(\ln \relax (x )-x +\ln \left (\ln \left (x^{2}-\frac {x}{3}-\frac {\ln \relax (x )}{2}+1\right )-\frac {i \left (\pi \,\mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (i \left (-x^{2}+\frac {x}{3}+\frac {\ln \relax (x )}{2}-1\right )\right ) \mathrm {csgn}\left (\frac {i \left (-x^{2}+\frac {x}{3}+\frac {\ln \relax (x )}{2}-1\right )}{x}\right )-\pi \,\mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (\frac {i \left (-x^{2}+\frac {x}{3}+\frac {\ln \relax (x )}{2}-1\right )}{x}\right )^{2}+\pi \,\mathrm {csgn}\left (i \left (-x^{2}+\frac {x}{3}+\frac {\ln \relax (x )}{2}-1\right )\right ) \mathrm {csgn}\left (\frac {i \left (-x^{2}+\frac {x}{3}+\frac {\ln \relax (x )}{2}-1\right )}{x}\right )^{2}-\pi \mathrm {csgn}\left (\frac {i \left (-x^{2}+\frac {x}{3}+\frac {\ln \relax (x )}{2}-1\right )}{x}\right )^{3}+2 i \ln \relax (2)+2 i \ln \relax (3)-2 i \ln \relax (x )\right )}{2}\right )\) | \(191\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.39, size = 27, normalized size = 0.84 \begin {gather*} -x + \log \relax (x) + \log \left (\log \left (6 \, x^{2} - 2 \, x - 3 \, \log \relax (x) + 6\right ) - \log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 9.24, size = 27, normalized size = 0.84 \begin {gather*} \ln \left (\ln \left (-\frac {2\,x+3\,\ln \relax (x)-6\,x^2-6}{x}\right )\right )-x+\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.67, size = 24, normalized size = 0.75 \begin {gather*} - x + \log {\relax (x )} + \log {\left (\log {\left (\frac {6 x^{2} - 2 x - 3 \log {\relax (x )} + 6}{x} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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