Optimal. Leaf size=25 \[ \frac {12}{x^2}-\log \left (9 \left (-3+\frac {1}{3} x (1+x+\log (x))\right )^2\right ) \]
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Rubi [F] time = 0.54, 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 {216-24 x-24 x^2-4 x^3-4 x^4+\left (-24 x-2 x^3\right ) \log (x)}{-9 x^3+x^4+x^5+x^4 \log (x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \left (-108+12 x+12 x^2+2 x^3+2 x^4+12 x \log (x)+x^3 \log (x)\right )}{9 x^3-x^4-x^5-x^4 \log (x)} \, dx\\ &=2 \int \frac {-108+12 x+12 x^2+2 x^3+2 x^4+12 x \log (x)+x^3 \log (x)}{9 x^3-x^4-x^5-x^4 \log (x)} \, dx\\ &=2 \int \left (\frac {-12-x^2}{x^3}+\frac {-9-x-x^2}{x \left (-9+x+x^2+x \log (x)\right )}\right ) \, dx\\ &=2 \int \frac {-12-x^2}{x^3} \, dx+2 \int \frac {-9-x-x^2}{x \left (-9+x+x^2+x \log (x)\right )} \, dx\\ &=2 \int \left (-\frac {12}{x^3}-\frac {1}{x}\right ) \, dx+2 \int \left (\frac {1}{9-x-x^2-x \log (x)}-\frac {9}{x \left (-9+x+x^2+x \log (x)\right )}-\frac {x}{-9+x+x^2+x \log (x)}\right ) \, dx\\ &=\frac {12}{x^2}-2 \log (x)+2 \int \frac {1}{9-x-x^2-x \log (x)} \, dx-2 \int \frac {x}{-9+x+x^2+x \log (x)} \, dx-18 \int \frac {1}{x \left (-9+x+x^2+x \log (x)\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.10, size = 24, normalized size = 0.96 \begin {gather*} -2 \left (-\frac {6}{x^2}+\log \left (9-x-x^2-x \log (x)\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.01, size = 32, normalized size = 1.28 \begin {gather*} -\frac {2 \, {\left (x^{2} \log \relax (x) + x^{2} \log \left (\frac {x^{2} + x \log \relax (x) + x - 9}{x}\right ) - 6\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 19, normalized size = 0.76 \begin {gather*} \frac {12}{x^{2}} - 2 \, \log \left (x^{2} + x \log \relax (x) + x - 9\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 20, normalized size = 0.80
method | result | size |
norman | \(\frac {12}{x^{2}}-2 \ln \left (x \ln \relax (x )+x^{2}+x -9\right )\) | \(20\) |
risch | \(-\frac {2 \left (x^{2} \ln \relax (x )-6\right )}{x^{2}}-2 \ln \left (\ln \relax (x )+\frac {x^{2}+x -9}{x}\right )\) | \(31\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 27, normalized size = 1.08 \begin {gather*} \frac {12}{x^{2}} - 2 \, \log \relax (x) - 2 \, \log \left (\frac {x^{2} + x \log \relax (x) + x - 9}{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.72, size = 27, normalized size = 1.08 \begin {gather*} \frac {12}{x^2}-2\,\ln \relax (x)-2\,\ln \left (\frac {x+x\,\ln \relax (x)+x^2-9}{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.20, size = 24, normalized size = 0.96 \begin {gather*} - 2 \log {\relax (x )} - 2 \log {\left (\log {\relax (x )} + \frac {x^{2} + x - 9}{x} \right )} + \frac {12}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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