Integrand size = 75, antiderivative size = 29 \[ \int \frac {-1216-64 x+(-1600-768 x) \log (x)+320 x^2 \log ^2(x)}{\left (-30+6 x+\left (25 x-11 x^2\right ) \log (x)+5 x^3 \log ^2(x)\right ) \log ^5\left (\frac {24-20 x \log (x)}{5-x+x^2 \log (x)}\right )} \, dx=\frac {16}{\log ^4\left (\frac {4}{5-\frac {25+x}{5+\frac {1}{1-x \log (x)}}}\right )} \]
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\[ \int \frac {-1216-64 x+(-1600-768 x) \log (x)+320 x^2 \log ^2(x)}{\left (-30+6 x+\left (25 x-11 x^2\right ) \log (x)+5 x^3 \log ^2(x)\right ) \log ^5\left (\frac {24-20 x \log (x)}{5-x+x^2 \log (x)}\right )} \, dx=\int \frac {-1216-64 x+(-1600-768 x) \log (x)+320 x^2 \log ^2(x)}{\left (-30+6 x+\left (25 x-11 x^2\right ) \log (x)+5 x^3 \log ^2(x)\right ) \log ^5\left (\frac {24-20 x \log (x)}{5-x+x^2 \log (x)}\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {1216+64 x-(-1600-768 x) \log (x)-320 x^2 \log ^2(x)}{\left (30-6 x-\left (25 x-11 x^2\right ) \log (x)-5 x^3 \log ^2(x)\right ) \log ^5\left (-\frac {4 (-6+5 x \log (x))}{5-x+x^2 \log (x)}\right )} \, dx \\ & = \int \frac {64 \left (19+x+25 \log (x)+12 x \log (x)-5 x^2 \log ^2(x)\right )}{\left (30-6 x-\left (25 x-11 x^2\right ) \log (x)-5 x^3 \log ^2(x)\right ) \log ^5\left (-\frac {4 (-6+5 x \log (x))}{5-x+x^2 \log (x)}\right )} \, dx \\ & = 64 \int \frac {19+x+25 \log (x)+12 x \log (x)-5 x^2 \log ^2(x)}{\left (30-6 x-\left (25 x-11 x^2\right ) \log (x)-5 x^3 \log ^2(x)\right ) \log ^5\left (-\frac {4 (-6+5 x \log (x))}{5-x+x^2 \log (x)}\right )} \, dx \\ & = 64 \int \left (\frac {19}{\left (30-6 x-25 x \log (x)+11 x^2 \log (x)-5 x^3 \log ^2(x)\right ) \log ^5\left (-\frac {4 (-6+5 x \log (x))}{5-x+x^2 \log (x)}\right )}+\frac {x}{\left (30-6 x-25 x \log (x)+11 x^2 \log (x)-5 x^3 \log ^2(x)\right ) \log ^5\left (-\frac {4 (-6+5 x \log (x))}{5-x+x^2 \log (x)}\right )}+\frac {25 \log (x)}{\left (30-6 x-25 x \log (x)+11 x^2 \log (x)-5 x^3 \log ^2(x)\right ) \log ^5\left (-\frac {4 (-6+5 x \log (x))}{5-x+x^2 \log (x)}\right )}+\frac {12 x \log (x)}{\left (30-6 x-25 x \log (x)+11 x^2 \log (x)-5 x^3 \log ^2(x)\right ) \log ^5\left (-\frac {4 (-6+5 x \log (x))}{5-x+x^2 \log (x)}\right )}+\frac {5 x^2 \log ^2(x)}{\left (-30+6 x+25 x \log (x)-11 x^2 \log (x)+5 x^3 \log ^2(x)\right ) \log ^5\left (-\frac {4 (-6+5 x \log (x))}{5-x+x^2 \log (x)}\right )}\right ) \, dx \\ & = 64 \int \frac {x}{\left (30-6 x-25 x \log (x)+11 x^2 \log (x)-5 x^3 \log ^2(x)\right ) \log ^5\left (-\frac {4 (-6+5 x \log (x))}{5-x+x^2 \log (x)}\right )} \, dx+320 \int \frac {x^2 \log ^2(x)}{\left (-30+6 x+25 x \log (x)-11 x^2 \log (x)+5 x^3 \log ^2(x)\right ) \log ^5\left (-\frac {4 (-6+5 x \log (x))}{5-x+x^2 \log (x)}\right )} \, dx+768 \int \frac {x \log (x)}{\left (30-6 x-25 x \log (x)+11 x^2 \log (x)-5 x^3 \log ^2(x)\right ) \log ^5\left (-\frac {4 (-6+5 x \log (x))}{5-x+x^2 \log (x)}\right )} \, dx+1216 \int \frac {1}{\left (30-6 x-25 x \log (x)+11 x^2 \log (x)-5 x^3 \log ^2(x)\right ) \log ^5\left (-\frac {4 (-6+5 x \log (x))}{5-x+x^2 \log (x)}\right )} \, dx+1600 \int \frac {\log (x)}{\left (30-6 x-25 x \log (x)+11 x^2 \log (x)-5 x^3 \log ^2(x)\right ) \log ^5\left (-\frac {4 (-6+5 x \log (x))}{5-x+x^2 \log (x)}\right )} \, dx \\ \end{align*}
Time = 0.37 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.90 \[ \int \frac {-1216-64 x+(-1600-768 x) \log (x)+320 x^2 \log ^2(x)}{\left (-30+6 x+\left (25 x-11 x^2\right ) \log (x)+5 x^3 \log ^2(x)\right ) \log ^5\left (\frac {24-20 x \log (x)}{5-x+x^2 \log (x)}\right )} \, dx=\frac {16}{\log ^4\left (\frac {24-20 x \log (x)}{5-x+x^2 \log (x)}\right )} \]
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Time = 10.98 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.97
method | result | size |
parallelrisch | \(\frac {16}{\ln \left (-\frac {4 \left (5 x \ln \left (x \right )-6\right )}{x^{2} \ln \left (x \right )+5-x}\right )^{4}}\) | \(28\) |
default | \(\frac {256}{{\left (-2 \pi \operatorname {csgn}\left (\frac {i \left (x \ln \left (x \right )-\frac {6}{5}\right )}{x^{2} \ln \left (x \right )+5-x}\right )^{2}-\pi \,\operatorname {csgn}\left (i \left (x \ln \left (x \right )-\frac {6}{5}\right )\right ) \operatorname {csgn}\left (\frac {i}{x^{2} \ln \left (x \right )+5-x}\right ) \operatorname {csgn}\left (\frac {i \left (x \ln \left (x \right )-\frac {6}{5}\right )}{x^{2} \ln \left (x \right )+5-x}\right )+\pi \,\operatorname {csgn}\left (i \left (x \ln \left (x \right )-\frac {6}{5}\right )\right ) \operatorname {csgn}\left (\frac {i \left (x \ln \left (x \right )-\frac {6}{5}\right )}{x^{2} \ln \left (x \right )+5-x}\right )^{2}+\pi \,\operatorname {csgn}\left (\frac {i}{x^{2} \ln \left (x \right )+5-x}\right ) \operatorname {csgn}\left (\frac {i \left (x \ln \left (x \right )-\frac {6}{5}\right )}{x^{2} \ln \left (x \right )+5-x}\right )^{2}+\pi \operatorname {csgn}\left (\frac {i \left (x \ln \left (x \right )-\frac {6}{5}\right )}{x^{2} \ln \left (x \right )+5-x}\right )^{3}+2 \pi -2 i \ln \left (5\right )-4 i \ln \left (2\right )-2 i \ln \left (x \ln \left (x \right )-\frac {6}{5}\right )+2 i \ln \left (x^{2} \ln \left (x \right )+5-x \right )\right )}^{4}}\) | \(233\) |
risch | \(\frac {256}{{\left (-2 \pi \operatorname {csgn}\left (\frac {i \left (x \ln \left (x \right )-\frac {6}{5}\right )}{x^{2} \ln \left (x \right )+5-x}\right )^{2}-\pi \,\operatorname {csgn}\left (i \left (x \ln \left (x \right )-\frac {6}{5}\right )\right ) \operatorname {csgn}\left (\frac {i}{x^{2} \ln \left (x \right )+5-x}\right ) \operatorname {csgn}\left (\frac {i \left (x \ln \left (x \right )-\frac {6}{5}\right )}{x^{2} \ln \left (x \right )+5-x}\right )+\pi \,\operatorname {csgn}\left (i \left (x \ln \left (x \right )-\frac {6}{5}\right )\right ) \operatorname {csgn}\left (\frac {i \left (x \ln \left (x \right )-\frac {6}{5}\right )}{x^{2} \ln \left (x \right )+5-x}\right )^{2}+\pi \,\operatorname {csgn}\left (\frac {i}{x^{2} \ln \left (x \right )+5-x}\right ) \operatorname {csgn}\left (\frac {i \left (x \ln \left (x \right )-\frac {6}{5}\right )}{x^{2} \ln \left (x \right )+5-x}\right )^{2}+\pi \operatorname {csgn}\left (\frac {i \left (x \ln \left (x \right )-\frac {6}{5}\right )}{x^{2} \ln \left (x \right )+5-x}\right )^{3}+2 \pi -2 i \ln \left (5\right )-4 i \ln \left (2\right )-2 i \ln \left (x \ln \left (x \right )-\frac {6}{5}\right )+2 i \ln \left (x^{2} \ln \left (x \right )+5-x \right )\right )}^{4}}\) | \(233\) |
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Time = 0.25 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.93 \[ \int \frac {-1216-64 x+(-1600-768 x) \log (x)+320 x^2 \log ^2(x)}{\left (-30+6 x+\left (25 x-11 x^2\right ) \log (x)+5 x^3 \log ^2(x)\right ) \log ^5\left (\frac {24-20 x \log (x)}{5-x+x^2 \log (x)}\right )} \, dx=\frac {16}{\log \left (-\frac {4 \, {\left (5 \, x \log \left (x\right ) - 6\right )}}{x^{2} \log \left (x\right ) - x + 5}\right )^{4}} \]
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Time = 0.20 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.76 \[ \int \frac {-1216-64 x+(-1600-768 x) \log (x)+320 x^2 \log ^2(x)}{\left (-30+6 x+\left (25 x-11 x^2\right ) \log (x)+5 x^3 \log ^2(x)\right ) \log ^5\left (\frac {24-20 x \log (x)}{5-x+x^2 \log (x)}\right )} \, dx=\frac {16}{\log {\left (\frac {- 20 x \log {\left (x \right )} + 24}{x^{2} \log {\left (x \right )} - x + 5} \right )}^{4}} \]
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Result contains complex when optimal does not.
Time = 1.11 (sec) , antiderivative size = 332, normalized size of antiderivative = 11.45 \[ \int \frac {-1216-64 x+(-1600-768 x) \log (x)+320 x^2 \log ^2(x)}{\left (-30+6 x+\left (25 x-11 x^2\right ) \log (x)+5 x^3 \log ^2(x)\right ) \log ^5\left (\frac {24-20 x \log (x)}{5-x+x^2 \log (x)}\right )} \, dx=\frac {16}{\pi ^{4} - 8 i \, \pi ^{3} \log \left (2\right ) - 24 \, \pi ^{2} \log \left (2\right )^{2} + 32 i \, \pi \log \left (2\right )^{3} + 16 \, \log \left (2\right )^{4} - 4 \, {\left (i \, \pi + 2 \, \log \left (2\right ) + \log \left (5 \, x \log \left (x\right ) - 6\right )\right )} \log \left (x^{2} \log \left (x\right ) - x + 5\right )^{3} + \log \left (x^{2} \log \left (x\right ) - x + 5\right )^{4} - 4 \, {\left (-i \, \pi - 2 \, \log \left (2\right )\right )} \log \left (5 \, x \log \left (x\right ) - 6\right )^{3} + \log \left (5 \, x \log \left (x\right ) - 6\right )^{4} - 6 \, {\left (\pi ^{2} - 4 i \, \pi \log \left (2\right ) - 4 \, \log \left (2\right )^{2} + 2 \, {\left (-i \, \pi - 2 \, \log \left (2\right )\right )} \log \left (5 \, x \log \left (x\right ) - 6\right ) - \log \left (5 \, x \log \left (x\right ) - 6\right )^{2}\right )} \log \left (x^{2} \log \left (x\right ) - x + 5\right )^{2} - 6 \, {\left (\pi ^{2} - 4 i \, \pi \log \left (2\right ) - 4 \, \log \left (2\right )^{2}\right )} \log \left (5 \, x \log \left (x\right ) - 6\right )^{2} - 4 \, {\left (-i \, \pi ^{3} - 6 \, \pi ^{2} \log \left (2\right ) + 12 i \, \pi \log \left (2\right )^{2} + 8 \, \log \left (2\right )^{3} + 3 \, {\left (i \, \pi + 2 \, \log \left (2\right )\right )} \log \left (5 \, x \log \left (x\right ) - 6\right )^{2} + \log \left (5 \, x \log \left (x\right ) - 6\right )^{3} - 3 \, {\left (\pi ^{2} - 4 i \, \pi \log \left (2\right ) - 4 \, \log \left (2\right )^{2}\right )} \log \left (5 \, x \log \left (x\right ) - 6\right )\right )} \log \left (x^{2} \log \left (x\right ) - x + 5\right ) - 4 \, {\left (i \, \pi ^{3} + 6 \, \pi ^{2} \log \left (2\right ) - 12 i \, \pi \log \left (2\right )^{2} - 8 \, \log \left (2\right )^{3}\right )} \log \left (5 \, x \log \left (x\right ) - 6\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 603 vs. \(2 (27) = 54\).
Time = 0.57 (sec) , antiderivative size = 603, normalized size of antiderivative = 20.79 \[ \int \frac {-1216-64 x+(-1600-768 x) \log (x)+320 x^2 \log ^2(x)}{\left (-30+6 x+\left (25 x-11 x^2\right ) \log (x)+5 x^3 \log ^2(x)\right ) \log ^5\left (\frac {24-20 x \log (x)}{5-x+x^2 \log (x)}\right )} \, dx=\frac {16 \, {\left (5 \, x^{2} \log \left (x\right )^{2} - 12 \, x \log \left (x\right ) - x - 25 \, \log \left (x\right ) - 19\right )}}{5 \, x^{2} \log \left (x^{2} \log \left (x\right ) - x + 5\right )^{4} \log \left (x\right )^{2} - 20 \, x^{2} \log \left (x^{2} \log \left (x\right ) - x + 5\right )^{3} \log \left (-20 \, x \log \left (x\right ) + 24\right ) \log \left (x\right )^{2} + 30 \, x^{2} \log \left (x^{2} \log \left (x\right ) - x + 5\right )^{2} \log \left (-20 \, x \log \left (x\right ) + 24\right )^{2} \log \left (x\right )^{2} - 20 \, x^{2} \log \left (x^{2} \log \left (x\right ) - x + 5\right ) \log \left (-20 \, x \log \left (x\right ) + 24\right )^{3} \log \left (x\right )^{2} + 5 \, x^{2} \log \left (-20 \, x \log \left (x\right ) + 24\right )^{4} \log \left (x\right )^{2} - 12 \, x \log \left (x^{2} \log \left (x\right ) - x + 5\right )^{4} \log \left (x\right ) + 48 \, x \log \left (x^{2} \log \left (x\right ) - x + 5\right )^{3} \log \left (-20 \, x \log \left (x\right ) + 24\right ) \log \left (x\right ) - 72 \, x \log \left (x^{2} \log \left (x\right ) - x + 5\right )^{2} \log \left (-20 \, x \log \left (x\right ) + 24\right )^{2} \log \left (x\right ) + 48 \, x \log \left (x^{2} \log \left (x\right ) - x + 5\right ) \log \left (-20 \, x \log \left (x\right ) + 24\right )^{3} \log \left (x\right ) - 12 \, x \log \left (-20 \, x \log \left (x\right ) + 24\right )^{4} \log \left (x\right ) - x \log \left (x^{2} \log \left (x\right ) - x + 5\right )^{4} + 4 \, x \log \left (x^{2} \log \left (x\right ) - x + 5\right )^{3} \log \left (-20 \, x \log \left (x\right ) + 24\right ) - 6 \, x \log \left (x^{2} \log \left (x\right ) - x + 5\right )^{2} \log \left (-20 \, x \log \left (x\right ) + 24\right )^{2} + 4 \, x \log \left (x^{2} \log \left (x\right ) - x + 5\right ) \log \left (-20 \, x \log \left (x\right ) + 24\right )^{3} - x \log \left (-20 \, x \log \left (x\right ) + 24\right )^{4} - 25 \, \log \left (x^{2} \log \left (x\right ) - x + 5\right )^{4} \log \left (x\right ) + 100 \, \log \left (x^{2} \log \left (x\right ) - x + 5\right )^{3} \log \left (-20 \, x \log \left (x\right ) + 24\right ) \log \left (x\right ) - 150 \, \log \left (x^{2} \log \left (x\right ) - x + 5\right )^{2} \log \left (-20 \, x \log \left (x\right ) + 24\right )^{2} \log \left (x\right ) + 100 \, \log \left (x^{2} \log \left (x\right ) - x + 5\right ) \log \left (-20 \, x \log \left (x\right ) + 24\right )^{3} \log \left (x\right ) - 25 \, \log \left (-20 \, x \log \left (x\right ) + 24\right )^{4} \log \left (x\right ) - 19 \, \log \left (x^{2} \log \left (x\right ) - x + 5\right )^{4} + 76 \, \log \left (x^{2} \log \left (x\right ) - x + 5\right )^{3} \log \left (-20 \, x \log \left (x\right ) + 24\right ) - 114 \, \log \left (x^{2} \log \left (x\right ) - x + 5\right )^{2} \log \left (-20 \, x \log \left (x\right ) + 24\right )^{2} + 76 \, \log \left (x^{2} \log \left (x\right ) - x + 5\right ) \log \left (-20 \, x \log \left (x\right ) + 24\right )^{3} - 19 \, \log \left (-20 \, x \log \left (x\right ) + 24\right )^{4}} \]
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Time = 9.96 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.93 \[ \int \frac {-1216-64 x+(-1600-768 x) \log (x)+320 x^2 \log ^2(x)}{\left (-30+6 x+\left (25 x-11 x^2\right ) \log (x)+5 x^3 \log ^2(x)\right ) \log ^5\left (\frac {24-20 x \log (x)}{5-x+x^2 \log (x)}\right )} \, dx=\frac {16}{{\ln \left (-\frac {20\,x\,\ln \left (x\right )-24}{x^2\,\ln \left (x\right )-x+5}\right )}^4} \]
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