Integrand size = 150, antiderivative size = 27 \[ \int \frac {-180000+640 x+191250 x^2-680 x^3+\left (-144000 x-71488 x^2-152744 x^3+544 x^4\right ) \log \left (\frac {16+8 x+17 x^2}{16 x}\right )+\left (-800+850 x^2+\left (-640 x-320 x^2-680 x^3\right ) \log \left (\frac {16+8 x+17 x^2}{16 x}\right )\right ) \log \left (\log \left (\frac {16+8 x+17 x^2}{16 x}\right )\right )}{\left (16 x+8 x^2+17 x^3\right ) \log \left (\frac {16+8 x+17 x^2}{16 x}\right )} \, dx=\left (x-5 \left (-225+x-\log \left (\log \left (x+\frac {(4+x)^2}{16 x}\right )\right )\right )\right )^2 \]
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Time = 0.41 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.85, number of steps used = 4, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.027, Rules used = {1608, 6820, 12, 6818} \[ \int \frac {-180000+640 x+191250 x^2-680 x^3+\left (-144000 x-71488 x^2-152744 x^3+544 x^4\right ) \log \left (\frac {16+8 x+17 x^2}{16 x}\right )+\left (-800+850 x^2+\left (-640 x-320 x^2-680 x^3\right ) \log \left (\frac {16+8 x+17 x^2}{16 x}\right )\right ) \log \left (\log \left (\frac {16+8 x+17 x^2}{16 x}\right )\right )}{\left (16 x+8 x^2+17 x^3\right ) \log \left (\frac {16+8 x+17 x^2}{16 x}\right )} \, dx=\left (-4 x+5 \log \left (\log \left (\frac {17 x}{16}+\frac {1}{x}+\frac {1}{2}\right )\right )+1125\right )^2 \]
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Rule 12
Rule 1608
Rule 6818
Rule 6820
Rubi steps \begin{align*} \text {integral}& = \int \frac {-180000+640 x+191250 x^2-680 x^3+\left (-144000 x-71488 x^2-152744 x^3+544 x^4\right ) \log \left (\frac {16+8 x+17 x^2}{16 x}\right )+\left (-800+850 x^2+\left (-640 x-320 x^2-680 x^3\right ) \log \left (\frac {16+8 x+17 x^2}{16 x}\right )\right ) \log \left (\log \left (\frac {16+8 x+17 x^2}{16 x}\right )\right )}{x \left (16+8 x+17 x^2\right ) \log \left (\frac {16+8 x+17 x^2}{16 x}\right )} \, dx \\ & = \int \frac {2 \left (80-85 x^2+4 x \left (16+8 x+17 x^2\right ) \log \left (\frac {1}{2}+\frac {1}{x}+\frac {17 x}{16}\right )\right ) \left (-1125+4 x-5 \log \left (\log \left (\frac {1}{2}+\frac {1}{x}+\frac {17 x}{16}\right )\right )\right )}{x \left (16+8 x+17 x^2\right ) \log \left (\frac {1}{2}+\frac {1}{x}+\frac {17 x}{16}\right )} \, dx \\ & = 2 \int \frac {\left (80-85 x^2+4 x \left (16+8 x+17 x^2\right ) \log \left (\frac {1}{2}+\frac {1}{x}+\frac {17 x}{16}\right )\right ) \left (-1125+4 x-5 \log \left (\log \left (\frac {1}{2}+\frac {1}{x}+\frac {17 x}{16}\right )\right )\right )}{x \left (16+8 x+17 x^2\right ) \log \left (\frac {1}{2}+\frac {1}{x}+\frac {17 x}{16}\right )} \, dx \\ & = \left (1125-4 x+5 \log \left (\log \left (\frac {1}{2}+\frac {1}{x}+\frac {17 x}{16}\right )\right )\right )^2 \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(64\) vs. \(2(27)=54\).
Time = 0.06 (sec) , antiderivative size = 64, normalized size of antiderivative = 2.37 \[ \int \frac {-180000+640 x+191250 x^2-680 x^3+\left (-144000 x-71488 x^2-152744 x^3+544 x^4\right ) \log \left (\frac {16+8 x+17 x^2}{16 x}\right )+\left (-800+850 x^2+\left (-640 x-320 x^2-680 x^3\right ) \log \left (\frac {16+8 x+17 x^2}{16 x}\right )\right ) \log \left (\log \left (\frac {16+8 x+17 x^2}{16 x}\right )\right )}{\left (16 x+8 x^2+17 x^3\right ) \log \left (\frac {16+8 x+17 x^2}{16 x}\right )} \, dx=2 \left (-4500 x+8 x^2+5625 \log \left (\log \left (\frac {1}{2}+\frac {1}{x}+\frac {17 x}{16}\right )\right )-20 x \log \left (\log \left (\frac {1}{2}+\frac {1}{x}+\frac {17 x}{16}\right )\right )+\frac {25}{2} \log ^2\left (\log \left (\frac {1}{2}+\frac {1}{x}+\frac {17 x}{16}\right )\right )\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(70\) vs. \(2(26)=52\).
Time = 0.43 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.63
method | result | size |
parallelrisch | \(\frac {71872}{19}+16 x^{2}-40 \ln \left (\ln \left (\frac {17 x^{2}+8 x +16}{16 x}\right )\right ) x +25 {\ln \left (\ln \left (\frac {17 x^{2}+8 x +16}{16 x}\right )\right )}^{2}+11250 \ln \left (\ln \left (\frac {17 x^{2}+8 x +16}{16 x}\right )\right )-9000 x\) | \(71\) |
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Leaf count of result is larger than twice the leaf count of optimal. 54 vs. \(2 (23) = 46\).
Time = 0.24 (sec) , antiderivative size = 54, normalized size of antiderivative = 2.00 \[ \int \frac {-180000+640 x+191250 x^2-680 x^3+\left (-144000 x-71488 x^2-152744 x^3+544 x^4\right ) \log \left (\frac {16+8 x+17 x^2}{16 x}\right )+\left (-800+850 x^2+\left (-640 x-320 x^2-680 x^3\right ) \log \left (\frac {16+8 x+17 x^2}{16 x}\right )\right ) \log \left (\log \left (\frac {16+8 x+17 x^2}{16 x}\right )\right )}{\left (16 x+8 x^2+17 x^3\right ) \log \left (\frac {16+8 x+17 x^2}{16 x}\right )} \, dx=16 \, x^{2} - 10 \, {\left (4 \, x - 1125\right )} \log \left (\log \left (\frac {17 \, x^{2} + 8 \, x + 16}{16 \, x}\right )\right ) + 25 \, \log \left (\log \left (\frac {17 \, x^{2} + 8 \, x + 16}{16 \, x}\right )\right )^{2} - 9000 \, x \]
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Leaf count of result is larger than twice the leaf count of optimal. 66 vs. \(2 (20) = 40\).
Time = 0.22 (sec) , antiderivative size = 66, normalized size of antiderivative = 2.44 \[ \int \frac {-180000+640 x+191250 x^2-680 x^3+\left (-144000 x-71488 x^2-152744 x^3+544 x^4\right ) \log \left (\frac {16+8 x+17 x^2}{16 x}\right )+\left (-800+850 x^2+\left (-640 x-320 x^2-680 x^3\right ) \log \left (\frac {16+8 x+17 x^2}{16 x}\right )\right ) \log \left (\log \left (\frac {16+8 x+17 x^2}{16 x}\right )\right )}{\left (16 x+8 x^2+17 x^3\right ) \log \left (\frac {16+8 x+17 x^2}{16 x}\right )} \, dx=16 x^{2} - 40 x \log {\left (\log {\left (\frac {\frac {17 x^{2}}{16} + \frac {x}{2} + 1}{x} \right )} \right )} - 9000 x + 25 \log {\left (\log {\left (\frac {\frac {17 x^{2}}{16} + \frac {x}{2} + 1}{x} \right )} \right )}^{2} + 11250 \log {\left (\log {\left (\frac {\frac {17 x^{2}}{16} + \frac {x}{2} + 1}{x} \right )} \right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 62 vs. \(2 (23) = 46\).
Time = 0.32 (sec) , antiderivative size = 62, normalized size of antiderivative = 2.30 \[ \int \frac {-180000+640 x+191250 x^2-680 x^3+\left (-144000 x-71488 x^2-152744 x^3+544 x^4\right ) \log \left (\frac {16+8 x+17 x^2}{16 x}\right )+\left (-800+850 x^2+\left (-640 x-320 x^2-680 x^3\right ) \log \left (\frac {16+8 x+17 x^2}{16 x}\right )\right ) \log \left (\log \left (\frac {16+8 x+17 x^2}{16 x}\right )\right )}{\left (16 x+8 x^2+17 x^3\right ) \log \left (\frac {16+8 x+17 x^2}{16 x}\right )} \, dx=16 \, x^{2} - 10 \, {\left (4 \, x - 1125\right )} \log \left (-4 \, \log \left (2\right ) + \log \left (17 \, x^{2} + 8 \, x + 16\right ) - \log \left (x\right )\right ) + 25 \, \log \left (-4 \, \log \left (2\right ) + \log \left (17 \, x^{2} + 8 \, x + 16\right ) - \log \left (x\right )\right )^{2} - 9000 \, x \]
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Leaf count of result is larger than twice the leaf count of optimal. 97 vs. \(2 (23) = 46\).
Time = 0.38 (sec) , antiderivative size = 97, normalized size of antiderivative = 3.59 \[ \int \frac {-180000+640 x+191250 x^2-680 x^3+\left (-144000 x-71488 x^2-152744 x^3+544 x^4\right ) \log \left (\frac {16+8 x+17 x^2}{16 x}\right )+\left (-800+850 x^2+\left (-640 x-320 x^2-680 x^3\right ) \log \left (\frac {16+8 x+17 x^2}{16 x}\right )\right ) \log \left (\log \left (\frac {16+8 x+17 x^2}{16 x}\right )\right )}{\left (16 x+8 x^2+17 x^3\right ) \log \left (\frac {16+8 x+17 x^2}{16 x}\right )} \, dx=16 \, x^{2} - 25 \, \log \left (\log \left (17 \, x^{2} + 8 \, x + 16\right ) - \log \left (16 \, x\right )\right )^{2} - 10 \, {\left (4 \, x - 5 \, \log \left (\log \left (17 \, x^{2} + 8 \, x + 16\right ) - \log \left (16 \, x\right )\right )\right )} \log \left (\log \left (\frac {17 \, x^{2} + 8 \, x + 16}{16 \, x}\right )\right ) - 9000 \, x + 11250 \, \log \left (\log \left (17 \, x^{2} + 8 \, x + 16\right ) - \log \left (16 \, x\right )\right ) \]
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Time = 10.85 (sec) , antiderivative size = 66, normalized size of antiderivative = 2.44 \[ \int \frac {-180000+640 x+191250 x^2-680 x^3+\left (-144000 x-71488 x^2-152744 x^3+544 x^4\right ) \log \left (\frac {16+8 x+17 x^2}{16 x}\right )+\left (-800+850 x^2+\left (-640 x-320 x^2-680 x^3\right ) \log \left (\frac {16+8 x+17 x^2}{16 x}\right )\right ) \log \left (\log \left (\frac {16+8 x+17 x^2}{16 x}\right )\right )}{\left (16 x+8 x^2+17 x^3\right ) \log \left (\frac {16+8 x+17 x^2}{16 x}\right )} \, dx=16\,x^2-40\,x\,\ln \left (\ln \left (\frac {\frac {17\,x^2}{16}+\frac {x}{2}+1}{x}\right )\right )-9000\,x+25\,{\ln \left (\ln \left (\frac {\frac {17\,x^2}{16}+\frac {x}{2}+1}{x}\right )\right )}^2+11250\,\ln \left (\ln \left (\frac {\frac {17\,x^2}{16}+\frac {x}{2}+1}{x}\right )\right ) \]
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