Optimal. Leaf size=30 \[ \frac {1}{2} \left (-x+\frac {5 \left (x-\frac {x^2}{x-\log \left (x^2\right )}\right )}{x^3}\right ) \]
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Rubi [F]
time = 0.34, 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 {-10 x-x^5+\left (15 x+2 x^4\right ) \log \left (x^2\right )+\left (-10-x^3\right ) \log ^2\left (x^2\right )}{2 x^5-4 x^4 \log \left (x^2\right )+2 x^3 \log ^2\left (x^2\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 {-10 x-x^5+\left (15 x+2 x^4\right ) \log \left (x^2\right )+\left (-10-x^3\right ) \log ^2\left (x^2\right )}{2 x^3 \left (x-\log \left (x^2\right )\right )^2} \, dx\\ &=\frac {1}{2} \int \frac {-10 x-x^5+\left (15 x+2 x^4\right ) \log \left (x^2\right )+\left (-10-x^3\right ) \log ^2\left (x^2\right )}{x^3 \left (x-\log \left (x^2\right )\right )^2} \, dx\\ &=\frac {1}{2} \int \left (\frac {-10-x^3}{x^3}+\frac {5 (-2+x)}{x^2 \left (x-\log \left (x^2\right )\right )^2}+\frac {5}{x^2 \left (x-\log \left (x^2\right )\right )}\right ) \, dx\\ &=\frac {1}{2} \int \frac {-10-x^3}{x^3} \, dx+\frac {5}{2} \int \frac {-2+x}{x^2 \left (x-\log \left (x^2\right )\right )^2} \, dx+\frac {5}{2} \int \frac {1}{x^2 \left (x-\log \left (x^2\right )\right )} \, dx\\ &=\frac {1}{2} \int \left (-1-\frac {10}{x^3}\right ) \, dx+\frac {5}{2} \int \left (-\frac {2}{x^2 \left (x-\log \left (x^2\right )\right )^2}+\frac {1}{x \left (x-\log \left (x^2\right )\right )^2}\right ) \, dx+\frac {5}{2} \int \frac {1}{x^2 \left (x-\log \left (x^2\right )\right )} \, dx\\ &=\frac {5}{2 x^2}-\frac {x}{2}+\frac {5}{2} \int \frac {1}{x \left (x-\log \left (x^2\right )\right )^2} \, dx+\frac {5}{2} \int \frac {1}{x^2 \left (x-\log \left (x^2\right )\right )} \, dx-5 \int \frac {1}{x^2 \left (x-\log \left (x^2\right )\right )^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.05, size = 28, normalized size = 0.93 \begin {gather*} \frac {1}{2} \left (\frac {5}{x^2}-x+\frac {5}{x \left (-x+\log \left (x^2\right )\right )}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.43, size = 27, normalized size = 0.90
method | result | size |
risch | \(-\frac {x^{3}-5}{2 x^{2}}-\frac {5}{2 x \left (-\ln \left (x^{2}\right )+x \right )}\) | \(27\) |
norman | \(\frac {\frac {x^{3} \ln \left (x^{2}\right )}{2}-\frac {x^{4}}{2}-\frac {5 \ln \left (x^{2}\right )}{2}}{x^{2} \left (-\ln \left (x^{2}\right )+x \right )}\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 28, normalized size = 0.93 \begin {gather*} -\frac {x^{4} - 2 \, {\left (x^{3} - 5\right )} \log \left (x\right )}{2 \, {\left (x^{3} - 2 \, x^{2} \log \left (x\right )\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 32, normalized size = 1.07 \begin {gather*} -\frac {x^{4} - {\left (x^{3} - 5\right )} \log \left (x^{2}\right )}{2 \, {\left (x^{3} - x^{2} \log \left (x^{2}\right )\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 24, normalized size = 0.80 \begin {gather*} - \frac {x}{2} + \frac {5}{- 2 x^{2} + 2 x \log {\left (x^{2} \right )}} + \frac {5}{2 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 24, normalized size = 0.80 \begin {gather*} -\frac {1}{2} \, x - \frac {5}{2 \, {\left (x^{2} - x \log \left (x^{2}\right )\right )}} + \frac {5}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.15, size = 23, normalized size = 0.77 \begin {gather*} -\frac {x}{2}-\frac {5\,\ln \left (x^2\right )}{2\,x^2\,\left (x-\ln \left (x^2\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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