Integrand size = 52, antiderivative size = 26 \[ \int \frac {270-270 x^3+90 x^6-10 x^9-x^6 \log ^2(x)}{\left (-54 x+54 x^4-18 x^7+2 x^{10}\right ) \log ^2(x)} \, dx=5+\frac {x^2}{36 \left (\frac {3}{x^2}-x\right )^2}+\frac {5}{\log (x)} \]
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Time = 0.24 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.88, number of steps used = 7, number of rules used = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.115, Rules used = {6820, 12, 6874, 270, 2339, 30} \[ \int \frac {270-270 x^3+90 x^6-10 x^9-x^6 \log ^2(x)}{\left (-54 x+54 x^4-18 x^7+2 x^{10}\right ) \log ^2(x)} \, dx=\frac {x^6}{36 \left (3-x^3\right )^2}+\frac {5}{\log (x)} \]
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Rule 12
Rule 30
Rule 270
Rule 2339
Rule 6820
Rule 6874
Rubi steps \begin{align*} \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{align*}
Time = 0.06 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.12 \[ \int \frac {270-270 x^3+90 x^6-10 x^9-x^6 \log ^2(x)}{\left (-54 x+54 x^4-18 x^7+2 x^{10}\right ) \log ^2(x)} \, dx=\frac {1}{2} \left (-\frac {3-2 x^3}{6 \left (-3+x^3\right )^2}+\frac {10}{\log (x)}\right ) \]
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Time = 0.12 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.00
method | result | size |
default | \(\frac {5}{\ln \left (x \right )}+\frac {1}{4 \left (x^{3}-3\right )^{2}}+\frac {1}{6 x^{3}-18}\) | \(26\) |
parts | \(\frac {5}{\ln \left (x \right )}+\frac {1}{4 \left (x^{3}-3\right )^{2}}+\frac {1}{6 x^{3}-18}\) | \(26\) |
risch | \(\frac {2 x^{3}-3}{12 x^{6}-72 x^{3}+108}+\frac {5}{\ln \left (x \right )}\) | \(29\) |
parallelrisch | \(\frac {1620+x^{6} \ln \left (x \right )+180 x^{6}-1080 x^{3}}{36 \ln \left (x \right ) \left (x^{6}-6 x^{3}+9\right )}\) | \(37\) |
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Time = 0.26 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.54 \[ \int \frac {270-270 x^3+90 x^6-10 x^9-x^6 \log ^2(x)}{\left (-54 x+54 x^4-18 x^7+2 x^{10}\right ) \log ^2(x)} \, dx=\frac {60 \, x^{6} - 360 \, x^{3} + {\left (2 \, x^{3} - 3\right )} \log \left (x\right ) + 540}{12 \, {\left (x^{6} - 6 \, x^{3} + 9\right )} \log \left (x\right )} \]
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Time = 0.09 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.85 \[ \int \frac {270-270 x^3+90 x^6-10 x^9-x^6 \log ^2(x)}{\left (-54 x+54 x^4-18 x^7+2 x^{10}\right ) \log ^2(x)} \, dx=- \frac {3 - 2 x^{3}}{12 x^{6} - 72 x^{3} + 108} + \frac {5}{\log {\left (x \right )}} \]
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Time = 0.31 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.54 \[ \int \frac {270-270 x^3+90 x^6-10 x^9-x^6 \log ^2(x)}{\left (-54 x+54 x^4-18 x^7+2 x^{10}\right ) \log ^2(x)} \, dx=\frac {60 \, x^{6} - 360 \, x^{3} + {\left (2 \, x^{3} - 3\right )} \log \left (x\right ) + 540}{12 \, {\left (x^{6} - 6 \, x^{3} + 9\right )} \log \left (x\right )} \]
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Time = 0.26 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.08 \[ \int \frac {270-270 x^3+90 x^6-10 x^9-x^6 \log ^2(x)}{\left (-54 x+54 x^4-18 x^7+2 x^{10}\right ) \log ^2(x)} \, dx=\frac {2 \, x^{3} - 3}{12 \, {\left (x^{6} - 6 \, x^{3} + 9\right )}} + \frac {5}{\log \left (x\right )} \]
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Time = 12.38 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.04 \[ \int \frac {270-270 x^3+90 x^6-10 x^9-x^6 \log ^2(x)}{\left (-54 x+54 x^4-18 x^7+2 x^{10}\right ) \log ^2(x)} \, dx=\frac {5}{\ln \left (x\right )}+\frac {\frac {x^3}{6}-\frac {1}{4}}{x^6-6\,x^3+9} \]
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