Integrand size = 104, antiderivative size = 32 \[ \int \frac {150-150 x+(-100+100 x) \log (x)+450 x \log ^2(x)+\left (-50+50 x-300 x \log ^2(x)\right ) \log \left (x^2\right )+50 x \log ^2(x) \log ^2\left (x^2\right )}{\left (-9 x+9 x^2\right ) \log ^2(x)+\left (6 x-6 x^2\right ) \log ^2(x) \log \left (x^2\right )+\left (-x+x^2\right ) \log ^2(x) \log ^2\left (x^2\right )} \, dx=10 \left (-3+5 \left (\log \left (\frac {1-x}{3}\right )+\frac {1}{\log (x) \left (3-\log \left (x^2\right )\right )}\right )\right ) \]
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\[ \int \frac {150-150 x+(-100+100 x) \log (x)+450 x \log ^2(x)+\left (-50+50 x-300 x \log ^2(x)\right ) \log \left (x^2\right )+50 x \log ^2(x) \log ^2\left (x^2\right )}{\left (-9 x+9 x^2\right ) \log ^2(x)+\left (6 x-6 x^2\right ) \log ^2(x) \log \left (x^2\right )+\left (-x+x^2\right ) \log ^2(x) \log ^2\left (x^2\right )} \, dx=\int \frac {150-150 x+(-100+100 x) \log (x)+450 x \log ^2(x)+\left (-50+50 x-300 x \log ^2(x)\right ) \log \left (x^2\right )+50 x \log ^2(x) \log ^2\left (x^2\right )}{\left (-9 x+9 x^2\right ) \log ^2(x)+\left (6 x-6 x^2\right ) \log ^2(x) \log \left (x^2\right )+\left (-x+x^2\right ) \log ^2(x) \log ^2\left (x^2\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int 50 \left (\frac {1}{-1+x}+\frac {2}{x \log (x) \left (-3+\log \left (x^2\right )\right )^2}+\frac {1}{x \log ^2(x) \left (-3+\log \left (x^2\right )\right )}\right ) \, dx \\ & = 50 \int \left (\frac {1}{-1+x}+\frac {2}{x \log (x) \left (-3+\log \left (x^2\right )\right )^2}+\frac {1}{x \log ^2(x) \left (-3+\log \left (x^2\right )\right )}\right ) \, dx \\ & = 50 \log (1-x)+50 \int \frac {1}{x \log ^2(x) \left (-3+\log \left (x^2\right )\right )} \, dx+100 \int \frac {1}{x \log (x) \left (-3+\log \left (x^2\right )\right )^2} \, dx \\ \end{align*}
Time = 0.10 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.69 \[ \int \frac {150-150 x+(-100+100 x) \log (x)+450 x \log ^2(x)+\left (-50+50 x-300 x \log ^2(x)\right ) \log \left (x^2\right )+50 x \log ^2(x) \log ^2\left (x^2\right )}{\left (-9 x+9 x^2\right ) \log ^2(x)+\left (6 x-6 x^2\right ) \log ^2(x) \log \left (x^2\right )+\left (-x+x^2\right ) \log ^2(x) \log ^2\left (x^2\right )} \, dx=50 \left (\log (-1+x)+\frac {1}{3 \log (x)-\log (x) \log \left (x^2\right )}\right ) \]
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Time = 2.86 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.16
method | result | size |
parallelrisch | \(\frac {-1200+1200 \ln \left (-1+x \right ) \ln \left (x \right ) \ln \left (x^{2}\right )-3600 \ln \left (x \right ) \ln \left (-1+x \right )}{24 \left (\ln \left (x^{2}\right )-3\right ) \ln \left (x \right )}\) | \(37\) |
default | \(50 \ln \left (-1+x \right )-\frac {50}{\left (-2 \ln \left (x \right )+\ln \left (x^{2}\right )-3\right ) \ln \left (x \right )}+\frac {100}{\left (-2 \ln \left (x \right )+\ln \left (x^{2}\right )-3\right ) \left (\ln \left (x^{2}\right )-3\right )}\) | \(48\) |
parts | \(50 \ln \left (-1+x \right )-\frac {50}{\left (-2 \ln \left (x \right )+\ln \left (x^{2}\right )-3\right ) \ln \left (x \right )}+\frac {100}{\left (-2 \ln \left (x \right )+\ln \left (x^{2}\right )-3\right ) \left (\ln \left (x^{2}\right )-3\right )}\) | \(48\) |
risch | \(50 \ln \left (-1+x \right )-\frac {100 i}{\left (\pi \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )-2 \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}+\pi \operatorname {csgn}\left (i x^{2}\right )^{3}+4 i \ln \left (x \right )-6 i\right ) \ln \left (x \right )}\) | \(69\) |
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Time = 0.25 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.09 \[ \int \frac {150-150 x+(-100+100 x) \log (x)+450 x \log ^2(x)+\left (-50+50 x-300 x \log ^2(x)\right ) \log \left (x^2\right )+50 x \log ^2(x) \log ^2\left (x^2\right )}{\left (-9 x+9 x^2\right ) \log ^2(x)+\left (6 x-6 x^2\right ) \log ^2(x) \log \left (x^2\right )+\left (-x+x^2\right ) \log ^2(x) \log ^2\left (x^2\right )} \, dx=\frac {50 \, {\left (2 \, \log \left (x - 1\right ) \log \left (x\right )^{2} - 3 \, \log \left (x - 1\right ) \log \left (x\right ) - 1\right )}}{2 \, \log \left (x\right )^{2} - 3 \, \log \left (x\right )} \]
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Time = 0.08 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.59 \[ \int \frac {150-150 x+(-100+100 x) \log (x)+450 x \log ^2(x)+\left (-50+50 x-300 x \log ^2(x)\right ) \log \left (x^2\right )+50 x \log ^2(x) \log ^2\left (x^2\right )}{\left (-9 x+9 x^2\right ) \log ^2(x)+\left (6 x-6 x^2\right ) \log ^2(x) \log \left (x^2\right )+\left (-x+x^2\right ) \log ^2(x) \log ^2\left (x^2\right )} \, dx=50 \log {\left (x - 1 \right )} - \frac {50}{2 \log {\left (x \right )}^{2} - 3 \log {\left (x \right )}} \]
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Time = 0.23 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.69 \[ \int \frac {150-150 x+(-100+100 x) \log (x)+450 x \log ^2(x)+\left (-50+50 x-300 x \log ^2(x)\right ) \log \left (x^2\right )+50 x \log ^2(x) \log ^2\left (x^2\right )}{\left (-9 x+9 x^2\right ) \log ^2(x)+\left (6 x-6 x^2\right ) \log ^2(x) \log \left (x^2\right )+\left (-x+x^2\right ) \log ^2(x) \log ^2\left (x^2\right )} \, dx=-\frac {50}{2 \, \log \left (x\right )^{2} - 3 \, \log \left (x\right )} + 50 \, \log \left (x - 1\right ) \]
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Time = 0.30 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.72 \[ \int \frac {150-150 x+(-100+100 x) \log (x)+450 x \log ^2(x)+\left (-50+50 x-300 x \log ^2(x)\right ) \log \left (x^2\right )+50 x \log ^2(x) \log ^2\left (x^2\right )}{\left (-9 x+9 x^2\right ) \log ^2(x)+\left (6 x-6 x^2\right ) \log ^2(x) \log \left (x^2\right )+\left (-x+x^2\right ) \log ^2(x) \log ^2\left (x^2\right )} \, dx=-\frac {100}{3 \, {\left (2 \, \log \left (x\right ) - 3\right )}} + \frac {50}{3 \, \log \left (x\right )} + 50 \, \log \left (x - 1\right ) \]
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Time = 9.20 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.66 \[ \int \frac {150-150 x+(-100+100 x) \log (x)+450 x \log ^2(x)+\left (-50+50 x-300 x \log ^2(x)\right ) \log \left (x^2\right )+50 x \log ^2(x) \log ^2\left (x^2\right )}{\left (-9 x+9 x^2\right ) \log ^2(x)+\left (6 x-6 x^2\right ) \log ^2(x) \log \left (x^2\right )+\left (-x+x^2\right ) \log ^2(x) \log ^2\left (x^2\right )} \, dx=50\,\ln \left (x-1\right )-\frac {50}{\ln \left (x\right )\,\left (\ln \left (x^2\right )-3\right )} \]
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