Optimal. Leaf size=26 \[ 5+\frac {x^2}{36 \left (\frac {3}{x^2}-x\right )^2}+\frac {5}{\log (x)} \]
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Rubi [A]
time = 0.41, antiderivative size = 23, normalized size of antiderivative = 0.88, number of steps
used = 7, number of rules used = 6, integrand size = 52, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.115, Rules used = {6820, 12, 6874,
270, 2339, 30} \begin {gather*} \frac {x^6}{36 \left (3-x^3\right )^2}+\frac {5}{\log (x)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rule 270
Rule 2339
Rule 6820
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {10 \left (-3+x^3\right )^3+x^6 \log ^2(x)}{2 x \left (3-x^3\right )^3 \log ^2(x)} \, dx\\ &=\frac {1}{2} \int \frac {10 \left (-3+x^3\right )^3+x^6 \log ^2(x)}{x \left (3-x^3\right )^3 \log ^2(x)} \, dx\\ &=\frac {1}{2} \int \left (-\frac {x^5}{\left (-3+x^3\right )^3}-\frac {10}{x \log ^2(x)}\right ) \, dx\\ &=-\left (\frac {1}{2} \int \frac {x^5}{\left (-3+x^3\right )^3} \, dx\right )-5 \int \frac {1}{x \log ^2(x)} \, dx\\ &=\frac {x^6}{36 \left (3-x^3\right )^2}-5 \text {Subst}\left (\int \frac {1}{x^2} \, dx,x,\log (x)\right )\\ &=\frac {x^6}{36 \left (3-x^3\right )^2}+\frac {5}{\log (x)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 29, normalized size = 1.12 \begin {gather*} \frac {1}{2} \left (-\frac {3-2 x^3}{6 \left (-3+x^3\right )^2}+\frac {10}{\log (x)}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 26, normalized size = 1.00
method | result | size |
default | \(\frac {5}{\ln \left (x \right )}+\frac {1}{6 x^{3}-18}+\frac {1}{4 \left (x^{3}-3\right )^{2}}\) | \(26\) |
risch | \(\frac {2 x^{3}-3}{12 x^{6}-72 x^{3}+108}+\frac {5}{\ln \left (x \right )}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.52, size = 40, normalized size = 1.54 \begin {gather*} \frac {60 \, x^{6} - 360 \, x^{3} + {\left (2 \, x^{3} - 3\right )} \log \left (x\right ) + 540}{12 \, {\left (x^{6} - 6 \, x^{3} + 9\right )} \log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 40, normalized size = 1.54 \begin {gather*} \frac {60 \, x^{6} - 360 \, x^{3} + {\left (2 \, x^{3} - 3\right )} \log \left (x\right ) + 540}{12 \, {\left (x^{6} - 6 \, x^{3} + 9\right )} \log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 22, normalized size = 0.85 \begin {gather*} - \frac {3 - 2 x^{3}}{12 x^{6} - 72 x^{3} + 108} + \frac {5}{\log {\left (x \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.38, size = 28, normalized size = 1.08 \begin {gather*} \frac {2 \, x^{3} - 3}{12 \, {\left (x^{6} - 6 \, x^{3} + 9\right )}} + \frac {5}{\log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.65, size = 27, normalized size = 1.04 \begin {gather*} \frac {5}{\ln \left (x\right )}+\frac {\frac {x^3}{6}-\frac {1}{4}}{x^6-6\,x^3+9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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