Optimal. Leaf size=25 \[ -2+x-2 \left (\frac {1}{3}-2 x\right ) x+\frac {x}{-x+\log \left (\frac {1}{x^2}\right )} \]
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Rubi [F]
time = 0.16, 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 {6+x^2+24 x^3+\left (3-2 x-48 x^2\right ) \log \left (\frac {1}{x^2}\right )+(1+24 x) \log ^2\left (\frac {1}{x^2}\right )}{3 x^2-6 x \log \left (\frac {1}{x^2}\right )+3 \log ^2\left (\frac {1}{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 {6+x^2+24 x^3+\left (3-2 x-48 x^2\right ) \log \left (\frac {1}{x^2}\right )+(1+24 x) \log ^2\left (\frac {1}{x^2}\right )}{3 \left (x-\log \left (\frac {1}{x^2}\right )\right )^2} \, dx\\ &=\frac {1}{3} \int \frac {6+x^2+24 x^3+\left (3-2 x-48 x^2\right ) \log \left (\frac {1}{x^2}\right )+(1+24 x) \log ^2\left (\frac {1}{x^2}\right )}{\left (x-\log \left (\frac {1}{x^2}\right )\right )^2} \, dx\\ &=\frac {1}{3} \int \left (1+24 x+\frac {3 (2+x)}{\left (x-\log \left (\frac {1}{x^2}\right )\right )^2}-\frac {3}{x-\log \left (\frac {1}{x^2}\right )}\right ) \, dx\\ &=\frac {x}{3}+4 x^2+\int \frac {2+x}{\left (x-\log \left (\frac {1}{x^2}\right )\right )^2} \, dx-\int \frac {1}{x-\log \left (\frac {1}{x^2}\right )} \, dx\\ &=\frac {x}{3}+4 x^2+\int \left (\frac {2}{\left (x-\log \left (\frac {1}{x^2}\right )\right )^2}+\frac {x}{\left (x-\log \left (\frac {1}{x^2}\right )\right )^2}\right ) \, dx-\int \frac {1}{x-\log \left (\frac {1}{x^2}\right )} \, dx\\ &=\frac {x}{3}+4 x^2+2 \int \frac {1}{\left (x-\log \left (\frac {1}{x^2}\right )\right )^2} \, dx+\int \frac {x}{\left (x-\log \left (\frac {1}{x^2}\right )\right )^2} \, dx-\int \frac {1}{x-\log \left (\frac {1}{x^2}\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.07, size = 24, normalized size = 0.96 \begin {gather*} \frac {1}{3} \left (x+12 x^2+\frac {3 x}{-x+\log \left (\frac {1}{x^2}\right )}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 8.48, size = 23, normalized size = 0.92
method | result | size |
risch | \(4 x^{2}+\frac {x}{3}-\frac {x}{x -\ln \left (\frac {1}{x^{2}}\right )}\) | \(23\) |
norman | \(\frac {-\ln \left (\frac {1}{x^{2}}\right )+\frac {x^{2}}{3}+4 x^{3}-\frac {x \ln \left (\frac {1}{x^{2}}\right )}{3}-4 x^{2} \ln \left (\frac {1}{x^{2}}\right )}{x -\ln \left (\frac {1}{x^{2}}\right )}\) | \(45\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 33, normalized size = 1.32 \begin {gather*} \frac {12 \, x^{3} + x^{2} + 2 \, {\left (12 \, x^{2} + x\right )} \log \left (x\right ) - 3 \, x}{3 \, {\left (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 = 0.41, size = 37, normalized size = 1.48 \begin {gather*} \frac {12 \, x^{3} + x^{2} - {\left (12 \, x^{2} + x\right )} \log \left (\frac {1}{x^{2}}\right ) - 3 \, x}{3 \, {\left (x - \log \left (\frac {1}{x^{2}}\right )\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 17, normalized size = 0.68 \begin {gather*} 4 x^{2} + \frac {x}{3} + \frac {x}{- x + \log {\left (\frac {1}{x^{2}} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 20, normalized size = 0.80 \begin {gather*} 4 \, x^{2} + \frac {1}{3} \, x - \frac {x}{x + \log \left (x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.47, size = 25, normalized size = 1.00 \begin {gather*} \frac {x}{3}-\frac {\ln \left (\frac {1}{x^2}\right )}{x-\ln \left (\frac {1}{x^2}\right )}+4\,x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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