Optimal. Leaf size=18 \[ \frac {2 x}{-1+9 x^2+x \log \left (x^3\right )} \]
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Rubi [F] time = 0.32, 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 {-2-6 x-18 x^2}{1+81 x^4-2 x \log \left (x^3\right )+x^2 \log ^2\left (x^3\right )+3 x^2 \left (-6+6 x \log \left (x^3\right )\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 {2 \left (-1-3 x-9 x^2\right )}{\left (1-9 x^2-x \log \left (x^3\right )\right )^2} \, dx\\ &=2 \int \frac {-1-3 x-9 x^2}{\left (1-9 x^2-x \log \left (x^3\right )\right )^2} \, dx\\ &=2 \int \left (-\frac {1}{\left (-1+9 x^2+x \log \left (x^3\right )\right )^2}-\frac {3 x}{\left (-1+9 x^2+x \log \left (x^3\right )\right )^2}-\frac {9 x^2}{\left (-1+9 x^2+x \log \left (x^3\right )\right )^2}\right ) \, dx\\ &=-\left (2 \int \frac {1}{\left (-1+9 x^2+x \log \left (x^3\right )\right )^2} \, dx\right )-6 \int \frac {x}{\left (-1+9 x^2+x \log \left (x^3\right )\right )^2} \, dx-18 \int \frac {x^2}{\left (-1+9 x^2+x \log \left (x^3\right )\right )^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.10, size = 18, normalized size = 1.00 \begin {gather*} \frac {2 x}{-1+9 x^2+x \log \left (x^3\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.02, size = 17, normalized size = 0.94 \begin {gather*} \frac {2 \, x}{9 \, x^{2} + 3 \, x \log \relax (x) - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 17, normalized size = 0.94 \begin {gather*} \frac {2 \, x}{9 \, x^{2} + 3 \, x \log \relax (x) - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.16, size = 19, normalized size = 1.06
method | result | size |
norman | \(\frac {2 x}{9 x^{2}+x \ln \left (x^{3}\right )-1}\) | \(19\) |
default | \(\frac {2 x}{9 x^{2}+3 x \ln \relax (x )+x \left (\ln \left (x^{3}\right )-3 \ln \relax (x )\right )-1}\) | \(29\) |
risch | \(\frac {4 i x}{x \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 x \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+x \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i x^{3}\right )-x \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{3}\right )^{2}+x \pi \mathrm {csgn}\left (i x^{2}\right )^{3}-x \pi \,\mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i x^{3}\right )^{2}+x \pi \mathrm {csgn}\left (i x^{3}\right )^{3}+6 i x \ln \relax (x )+18 i x^{2}-2 i}\) | \(141\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.73, size = 17, normalized size = 0.94 \begin {gather*} \frac {2 \, x}{9 \, x^{2} + 3 \, x \log \relax (x) - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.03, size = 18, normalized size = 1.00 \begin {gather*} \frac {2\,x}{x\,\ln \left (x^3\right )+9\,x^2-1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 15, normalized size = 0.83 \begin {gather*} \frac {2 x}{9 x^{2} + x \log {\left (x^{3} \right )} - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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