Integrand size = 45, antiderivative size = 20 \[ \int \frac {-4-4 x+(-4-6 x) \log (x)-1296 x^3 \log ^3(x)}{\left (81 x^3+162 x^4+81 x^5\right ) \log ^3(x)} \, dx=\frac {2 \left (8+\frac {1}{81 x^2 \log ^2(x)}\right )}{1+x} \]
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\[ \int \frac {-4-4 x+(-4-6 x) \log (x)-1296 x^3 \log ^3(x)}{\left (81 x^3+162 x^4+81 x^5\right ) \log ^3(x)} \, dx=\int \frac {-4-4 x+(-4-6 x) \log (x)-1296 x^3 \log ^3(x)}{\left (81 x^3+162 x^4+81 x^5\right ) \log ^3(x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {-4-4 x+(-4-6 x) \log (x)-1296 x^3 \log ^3(x)}{x^3 \left (81+162 x+81 x^2\right ) \log ^3(x)} \, dx \\ & = \int \frac {-4-4 x+(-4-6 x) \log (x)-1296 x^3 \log ^3(x)}{81 x^3 (1+x)^2 \log ^3(x)} \, dx \\ & = \frac {1}{81} \int \frac {-4-4 x+(-4-6 x) \log (x)-1296 x^3 \log ^3(x)}{x^3 (1+x)^2 \log ^3(x)} \, dx \\ & = \frac {1}{81} \int \left (-\frac {1296}{(1+x)^2}-\frac {4}{x^3 (1+x) \log ^3(x)}-\frac {2 (2+3 x)}{x^3 (1+x)^2 \log ^2(x)}\right ) \, dx \\ & = \frac {16}{1+x}-\frac {2}{81} \int \frac {2+3 x}{x^3 (1+x)^2 \log ^2(x)} \, dx-\frac {4}{81} \int \frac {1}{x^3 (1+x) \log ^3(x)} \, dx \\ \end{align*}
Time = 0.13 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.95 \[ \int \frac {-4-4 x+(-4-6 x) \log (x)-1296 x^3 \log ^3(x)}{\left (81 x^3+162 x^4+81 x^5\right ) \log ^3(x)} \, dx=\frac {2 \left (648+\frac {1}{x^2 \log ^2(x)}\right )}{81 (1+x)} \]
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Time = 5.50 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.15
method | result | size |
risch | \(\frac {16}{1+x}+\frac {2}{81 x^{2} \left (1+x \right ) \ln \left (x \right )^{2}}\) | \(23\) |
norman | \(\frac {\frac {2}{81}+16 x^{2} \ln \left (x \right )^{2}}{x^{2} \left (1+x \right ) \ln \left (x \right )^{2}}\) | \(25\) |
parallelrisch | \(\frac {2+1296 x^{2} \ln \left (x \right )^{2}}{81 x^{2} \ln \left (x \right )^{2} \left (1+x \right )}\) | \(26\) |
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Time = 0.25 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.30 \[ \int \frac {-4-4 x+(-4-6 x) \log (x)-1296 x^3 \log ^3(x)}{\left (81 x^3+162 x^4+81 x^5\right ) \log ^3(x)} \, dx=\frac {2 \, {\left (648 \, x^{2} \log \left (x\right )^{2} + 1\right )}}{81 \, {\left (x^{3} + x^{2}\right )} \log \left (x\right )^{2}} \]
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Time = 0.08 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {-4-4 x+(-4-6 x) \log (x)-1296 x^3 \log ^3(x)}{\left (81 x^3+162 x^4+81 x^5\right ) \log ^3(x)} \, dx=\frac {2}{\left (81 x^{3} + 81 x^{2}\right ) \log {\left (x \right )}^{2}} + \frac {16}{x + 1} \]
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Time = 0.23 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.30 \[ \int \frac {-4-4 x+(-4-6 x) \log (x)-1296 x^3 \log ^3(x)}{\left (81 x^3+162 x^4+81 x^5\right ) \log ^3(x)} \, dx=\frac {2 \, {\left (648 \, x^{2} \log \left (x\right )^{2} + 1\right )}}{81 \, {\left (x^{3} + x^{2}\right )} \log \left (x\right )^{2}} \]
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Time = 0.26 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.45 \[ \int \frac {-4-4 x+(-4-6 x) \log (x)-1296 x^3 \log ^3(x)}{\left (81 x^3+162 x^4+81 x^5\right ) \log ^3(x)} \, dx=\frac {2}{81 \, {\left (x^{3} \log \left (x\right )^{2} + x^{2} \log \left (x\right )^{2}\right )}} + \frac {16}{x + 1} \]
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Time = 10.07 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.25 \[ \int \frac {-4-4 x+(-4-6 x) \log (x)-1296 x^3 \log ^3(x)}{\left (81 x^3+162 x^4+81 x^5\right ) \log ^3(x)} \, dx=-\frac {16\,x^3\,{\ln \left (x\right )}^2-\frac {2}{81}}{x^2\,{\ln \left (x\right )}^2\,\left (x+1\right )} \]
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