Optimal. Leaf size=18 \[ \frac {3 (29+x)}{\left (-\frac {1}{x}+x\right ) \log (x)} \]
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Rubi [F] time = 0.23, 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 {87+3 x-87 x^2-3 x^3+\left (-87-6 x-87 x^2\right ) \log (x)}{\left (1-2 x^2+x^4\right ) \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 {87+3 x-87 x^2-3 x^3+\left (-87-6 x-87 x^2\right ) \log (x)}{\left (-1+x^2\right )^2 \log ^2(x)} \, dx\\ &=\int \left (-\frac {3 (29+x)}{\left (-1+x^2\right ) \log ^2(x)}-\frac {3 \left (29+2 x+29 x^2\right )}{\left (-1+x^2\right )^2 \log (x)}\right ) \, dx\\ &=-\left (3 \int \frac {29+x}{\left (-1+x^2\right ) \log ^2(x)} \, dx\right )-3 \int \frac {29+2 x+29 x^2}{\left (-1+x^2\right )^2 \log (x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.08, size = 17, normalized size = 0.94 \begin {gather*} \frac {3 x (29+x)}{\left (-1+x^2\right ) \log (x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.23, size = 20, normalized size = 1.11 \begin {gather*} \frac {3 \, {\left (x^{2} + 29 \, x\right )}}{{\left (x^{2} - 1\right )} \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 = 22, normalized size = 1.22 \begin {gather*} \frac {3 \, {\left (x^{2} + 29 \, x\right )}}{x^{2} \log \relax (x) - \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 18, normalized size = 1.00
method | result | size |
risch | \(\frac {3 x \left (x +29\right )}{\left (x^{2}-1\right ) \ln \relax (x )}\) | \(18\) |
norman | \(\frac {3 x^{2}+87 x}{\left (x^{2}-1\right ) \ln \relax (x )}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 20, normalized size = 1.11 \begin {gather*} \frac {3 \, {\left (x^{2} + 29 \, x\right )}}{{\left (x^{2} - 1\right )} \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 8.56, size = 17, normalized size = 0.94 \begin {gather*} \frac {3\,x\,\left (x+29\right )}{\ln \relax (x)\,\left (x^2-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 15, normalized size = 0.83 \begin {gather*} \frac {3 x^{2} + 87 x}{\left (x^{2} - 1\right ) \log {\relax (x )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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