Optimal. Leaf size=29 \[ \frac {3 \log ^2\left (2+\frac {5}{x^2}+x-x^2\right )}{x^2 \log ^2\left (\frac {2}{x}\right )} \]
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Rubi [F] time = 3.38, 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 {\left (-30-12 x^2-6 x^3+6 x^4\right ) \log ^2\left (\frac {5+2 x^2+x^3-x^4}{x^2}\right )+\log \left (\frac {2}{x}\right ) \left (\left (60-6 x^3+12 x^4\right ) \log \left (\frac {5+2 x^2+x^3-x^4}{x^2}\right )+\left (30+12 x^2+6 x^3-6 x^4\right ) \log ^2\left (\frac {5+2 x^2+x^3-x^4}{x^2}\right )\right )}{\left (-5 x^3-2 x^5-x^6+x^7\right ) \log ^3\left (\frac {2}{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 {-\left (\left (-30-12 x^2-6 x^3+6 x^4\right ) \log ^2\left (\frac {5+2 x^2+x^3-x^4}{x^2}\right )\right )-\log \left (\frac {2}{x}\right ) \left (\left (60-6 x^3+12 x^4\right ) \log \left (\frac {5+2 x^2+x^3-x^4}{x^2}\right )+\left (30+12 x^2+6 x^3-6 x^4\right ) \log ^2\left (\frac {5+2 x^2+x^3-x^4}{x^2}\right )\right )}{x^3 \left (5+2 x^2+x^3-x^4\right ) \log ^3\left (\frac {2}{x}\right )} \, dx\\ &=\int \left (\frac {6 \left (10-x^3+2 x^4\right ) \log \left (2+\frac {5}{x^2}+x-x^2\right )}{x^3 \left (-5-2 x^2-x^3+x^4\right ) \log ^2\left (\frac {2}{x}\right )}-\frac {6 \left (-1+\log \left (\frac {2}{x}\right )\right ) \log ^2\left (2+\frac {5}{x^2}+x-x^2\right )}{x^3 \log ^3\left (\frac {2}{x}\right )}\right ) \, dx\\ &=6 \int \frac {\left (10-x^3+2 x^4\right ) \log \left (2+\frac {5}{x^2}+x-x^2\right )}{x^3 \left (-5-2 x^2-x^3+x^4\right ) \log ^2\left (\frac {2}{x}\right )} \, dx-6 \int \frac {\left (-1+\log \left (\frac {2}{x}\right )\right ) \log ^2\left (2+\frac {5}{x^2}+x-x^2\right )}{x^3 \log ^3\left (\frac {2}{x}\right )} \, dx\\ &=6 \int \left (-\frac {2 \log \left (2+\frac {5}{x^2}+x-x^2\right )}{x^3 \log ^2\left (\frac {2}{x}\right )}+\frac {4 \log \left (2+\frac {5}{x^2}+x-x^2\right )}{5 x \log ^2\left (\frac {2}{x}\right )}-\frac {\left (15-28 x-4 x^2+4 x^3\right ) \log \left (2+\frac {5}{x^2}+x-x^2\right )}{5 \left (-5-2 x^2-x^3+x^4\right ) \log ^2\left (\frac {2}{x}\right )}\right ) \, dx-6 \int \left (-\frac {\log ^2\left (2+\frac {5}{x^2}+x-x^2\right )}{x^3 \log ^3\left (\frac {2}{x}\right )}+\frac {\log ^2\left (2+\frac {5}{x^2}+x-x^2\right )}{x^3 \log ^2\left (\frac {2}{x}\right )}\right ) \, dx\\ &=-\left (\frac {6}{5} \int \frac {\left (15-28 x-4 x^2+4 x^3\right ) \log \left (2+\frac {5}{x^2}+x-x^2\right )}{\left (-5-2 x^2-x^3+x^4\right ) \log ^2\left (\frac {2}{x}\right )} \, dx\right )+\frac {24}{5} \int \frac {\log \left (2+\frac {5}{x^2}+x-x^2\right )}{x \log ^2\left (\frac {2}{x}\right )} \, dx+6 \int \frac {\log ^2\left (2+\frac {5}{x^2}+x-x^2\right )}{x^3 \log ^3\left (\frac {2}{x}\right )} \, dx-6 \int \frac {\log ^2\left (2+\frac {5}{x^2}+x-x^2\right )}{x^3 \log ^2\left (\frac {2}{x}\right )} \, dx-12 \int \frac {\log \left (2+\frac {5}{x^2}+x-x^2\right )}{x^3 \log ^2\left (\frac {2}{x}\right )} \, dx\\ &=-\left (\frac {6}{5} \int \left (\frac {15 \log \left (2+\frac {5}{x^2}+x-x^2\right )}{\left (-5-2 x^2-x^3+x^4\right ) \log ^2\left (\frac {2}{x}\right )}-\frac {28 x \log \left (2+\frac {5}{x^2}+x-x^2\right )}{\left (-5-2 x^2-x^3+x^4\right ) \log ^2\left (\frac {2}{x}\right )}-\frac {4 x^2 \log \left (2+\frac {5}{x^2}+x-x^2\right )}{\left (-5-2 x^2-x^3+x^4\right ) \log ^2\left (\frac {2}{x}\right )}+\frac {4 x^3 \log \left (2+\frac {5}{x^2}+x-x^2\right )}{\left (-5-2 x^2-x^3+x^4\right ) \log ^2\left (\frac {2}{x}\right )}\right ) \, dx\right )+\frac {24}{5} \int \frac {\log \left (2+\frac {5}{x^2}+x-x^2\right )}{x \log ^2\left (\frac {2}{x}\right )} \, dx+6 \int \frac {\log ^2\left (2+\frac {5}{x^2}+x-x^2\right )}{x^3 \log ^3\left (\frac {2}{x}\right )} \, dx-6 \int \frac {\log ^2\left (2+\frac {5}{x^2}+x-x^2\right )}{x^3 \log ^2\left (\frac {2}{x}\right )} \, dx-12 \int \frac {\log \left (2+\frac {5}{x^2}+x-x^2\right )}{x^3 \log ^2\left (\frac {2}{x}\right )} \, dx\\ &=\frac {24}{5} \int \frac {\log \left (2+\frac {5}{x^2}+x-x^2\right )}{x \log ^2\left (\frac {2}{x}\right )} \, dx+\frac {24}{5} \int \frac {x^2 \log \left (2+\frac {5}{x^2}+x-x^2\right )}{\left (-5-2 x^2-x^3+x^4\right ) \log ^2\left (\frac {2}{x}\right )} \, dx-\frac {24}{5} \int \frac {x^3 \log \left (2+\frac {5}{x^2}+x-x^2\right )}{\left (-5-2 x^2-x^3+x^4\right ) \log ^2\left (\frac {2}{x}\right )} \, dx+6 \int \frac {\log ^2\left (2+\frac {5}{x^2}+x-x^2\right )}{x^3 \log ^3\left (\frac {2}{x}\right )} \, dx-6 \int \frac {\log ^2\left (2+\frac {5}{x^2}+x-x^2\right )}{x^3 \log ^2\left (\frac {2}{x}\right )} \, dx-12 \int \frac {\log \left (2+\frac {5}{x^2}+x-x^2\right )}{x^3 \log ^2\left (\frac {2}{x}\right )} \, dx-18 \int \frac {\log \left (2+\frac {5}{x^2}+x-x^2\right )}{\left (-5-2 x^2-x^3+x^4\right ) \log ^2\left (\frac {2}{x}\right )} \, dx+\frac {168}{5} \int \frac {x \log \left (2+\frac {5}{x^2}+x-x^2\right )}{\left (-5-2 x^2-x^3+x^4\right ) \log ^2\left (\frac {2}{x}\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [F] time = 0.15, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (-30-12 x^2-6 x^3+6 x^4\right ) \log ^2\left (\frac {5+2 x^2+x^3-x^4}{x^2}\right )+\log \left (\frac {2}{x}\right ) \left (\left (60-6 x^3+12 x^4\right ) \log \left (\frac {5+2 x^2+x^3-x^4}{x^2}\right )+\left (30+12 x^2+6 x^3-6 x^4\right ) \log ^2\left (\frac {5+2 x^2+x^3-x^4}{x^2}\right )\right )}{\left (-5 x^3-2 x^5-x^6+x^7\right ) \log ^3\left (\frac {2}{x}\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.57, size = 36, normalized size = 1.24 \begin {gather*} \frac {3 \, \log \left (-\frac {x^{4} - x^{3} - 2 \, x^{2} - 5}{x^{2}}\right )^{2}}{x^{2} \log \left (\frac {2}{x}\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.30, size = 143, normalized size = 4.93 \begin {gather*} \frac {3 \, \log \left (-x^{4} + x^{3} + 2 \, x^{2} + 5\right )^{2}}{x^{2} \log \relax (2)^{2} - 2 \, x^{2} \log \relax (2) \log \relax (x) + x^{2} \log \relax (x)^{2}} - \frac {12 \, \log \left (-x^{4} + x^{3} + 2 \, x^{2} + 5\right ) \log \relax (x)}{x^{2} \log \relax (2)^{2} - 2 \, x^{2} \log \relax (2) \log \relax (x) + x^{2} \log \relax (x)^{2}} - \frac {12 \, {\left (\log \relax (2)^{2} - 2 \, \log \relax (2) \log \relax (x)\right )}}{x^{2} \log \relax (2)^{2} - 2 \, x^{2} \log \relax (2) \log \relax (x) + x^{2} \log \relax (x)^{2}} + \frac {12}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 2.35, size = 2291, normalized size = 79.00
method | result | size |
risch | \(\text {Expression too large to display}\) | \(2291\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.54, size = 75, normalized size = 2.59 \begin {gather*} \frac {3 \, {\left (\log \left (-x^{4} + x^{3} + 2 \, x^{2} + 5\right )^{2} - 4 \, \log \left (-x^{4} + x^{3} + 2 \, x^{2} + 5\right ) \log \relax (x) + 4 \, \log \relax (x)^{2}\right )}}{x^{2} \log \relax (2)^{2} - 2 \, x^{2} \log \relax (2) \log \relax (x) + x^{2} \log \relax (x)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.85, size = 35, normalized size = 1.21 \begin {gather*} \frac {3\,{\ln \left (\frac {-x^4+x^3+2\,x^2+5}{x^2}\right )}^2}{x^2\,{\ln \left (\frac {2}{x}\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.50, size = 31, normalized size = 1.07 \begin {gather*} \frac {3 \log {\left (\frac {- x^{4} + x^{3} + 2 x^{2} + 5}{x^{2}} \right )}^{2}}{x^{2} \log {\left (\frac {2}{x} \right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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