Optimal. Leaf size=29 \[ 4+\frac {4 \left (\frac {1}{2}+x-\frac {x}{\log ^2(2)-\frac {1}{3} x \log (x)}\right )}{x^2} \]
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Rubi [F] time = 0.88, 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 {-12 x^2+36 x \log ^2(2)+(-36-36 x) \log ^4(2)+\left (-24 x^2+\left (24 x+24 x^2\right ) \log ^2(2)\right ) \log (x)+\left (-4 x^2-4 x^3\right ) \log ^2(x)}{9 x^3 \log ^4(2)-6 x^4 \log ^2(2) \log (x)+x^5 \log ^2(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 {-12 x^2+36 x \log ^2(2)+(-36-36 x) \log ^4(2)+\left (-24 x^2+\left (24 x+24 x^2\right ) \log ^2(2)\right ) \log (x)+\left (-4 x^2-4 x^3\right ) \log ^2(x)}{x^3 \left (3 \log ^2(2)-x \log (x)\right )^2} \, dx\\ &=\int \left (-\frac {4 (1+x)}{x^3}-\frac {12 \left (x+3 \log ^2(2)\right )}{x^2 \left (-3 \log ^2(2)+x \log (x)\right )^2}-\frac {24}{x^2 \left (-3 \log ^2(2)+x \log (x)\right )}\right ) \, dx\\ &=-\left (4 \int \frac {1+x}{x^3} \, dx\right )-12 \int \frac {x+3 \log ^2(2)}{x^2 \left (-3 \log ^2(2)+x \log (x)\right )^2} \, dx-24 \int \frac {1}{x^2 \left (-3 \log ^2(2)+x \log (x)\right )} \, dx\\ &=\frac {2 (1+x)^2}{x^2}-12 \int \left (\frac {1}{x \left (-3 \log ^2(2)+x \log (x)\right )^2}+\frac {3 \log ^2(2)}{x^2 \left (-3 \log ^2(2)+x \log (x)\right )^2}\right ) \, dx-24 \int \frac {1}{x^2 \left (-3 \log ^2(2)+x \log (x)\right )} \, dx\\ &=\frac {2 (1+x)^2}{x^2}-12 \int \frac {1}{x \left (-3 \log ^2(2)+x \log (x)\right )^2} \, dx-24 \int \frac {1}{x^2 \left (-3 \log ^2(2)+x \log (x)\right )} \, dx-\left (36 \log ^2(2)\right ) \int \frac {1}{x^2 \left (-3 \log ^2(2)+x \log (x)\right )^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.20, size = 26, normalized size = 0.90 \begin {gather*} -\frac {2 \left (-1+x \left (-2-\frac {6}{-3 \log ^2(2)+x \log (x)}\right )\right )}{x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.51, size = 47, normalized size = 1.62 \begin {gather*} \frac {2 \, {\left (3 \, {\left (2 \, x + 1\right )} \log \relax (2)^{2} - {\left (2 \, x^{2} + x\right )} \log \relax (x) - 6 \, x\right )}}{3 \, x^{2} \log \relax (2)^{2} - x^{3} \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 30, normalized size = 1.03 \begin {gather*} -\frac {12}{3 \, x \log \relax (2)^{2} - x^{2} \log \relax (x)} + \frac {2 \, {\left (2 \, x + 1\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 31, normalized size = 1.07
method | result | size |
risch | \(\frac {4 x +2}{x^{2}}-\frac {12}{x \left (3 \ln \relax (2)^{2}-x \ln \relax (x )\right )}\) | \(31\) |
norman | \(\frac {\left (12 \ln \relax (2)^{2}-12\right ) x -4 x^{2} \ln \relax (x )+6 \ln \relax (2)^{2}-2 x \ln \relax (x )}{x^{2} \left (3 \ln \relax (2)^{2}-x \ln \relax (x )\right )}\) | \(48\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 48, normalized size = 1.66 \begin {gather*} \frac {2 \, {\left (6 \, {\left (\log \relax (2)^{2} - 1\right )} x + 3 \, \log \relax (2)^{2} - {\left (2 \, x^{2} + x\right )} \log \relax (x)\right )}}{3 \, x^{2} \log \relax (2)^{2} - x^{3} \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 8.26, size = 45, normalized size = 1.55 \begin {gather*} \frac {4\,x^2\,\ln \relax (x)+x\,\left (2\,\ln \relax (x)-12\,{\ln \relax (2)}^2+12\right )-6\,{\ln \relax (2)}^2}{x^2\,\left (x\,\ln \relax (x)-3\,{\ln \relax (2)}^2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 26, normalized size = 0.90 \begin {gather*} \frac {12}{x^{2} \log {\relax (x )} - 3 x \log {\relax (2 )}^{2}} - \frac {- 4 x - 2}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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