Integrand size = 90, antiderivative size = 23 \[ \int \frac {-4 \log ^2(5) \log \left (x^2\right )+2 \log ^2(5) \log ^2\left (x^2\right )+(-34+3 x) \log ^4\left (x^2\right )}{x^3 \log ^4(5)+\left (-34 x^3+2 x^4\right ) \log ^2(5) \log ^2\left (x^2\right )+\left (289 x^3-34 x^4+x^5\right ) \log ^4\left (x^2\right )} \, dx=\frac {1}{x^2 \left (17-x-\frac {\log ^2(5)}{\log ^2\left (x^2\right )}\right )} \]
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\[ \int \frac {-4 \log ^2(5) \log \left (x^2\right )+2 \log ^2(5) \log ^2\left (x^2\right )+(-34+3 x) \log ^4\left (x^2\right )}{x^3 \log ^4(5)+\left (-34 x^3+2 x^4\right ) \log ^2(5) \log ^2\left (x^2\right )+\left (289 x^3-34 x^4+x^5\right ) \log ^4\left (x^2\right )} \, dx=\int \frac {-4 \log ^2(5) \log \left (x^2\right )+2 \log ^2(5) \log ^2\left (x^2\right )+(-34+3 x) \log ^4\left (x^2\right )}{x^3 \log ^4(5)+\left (-34 x^3+2 x^4\right ) \log ^2(5) \log ^2\left (x^2\right )+\left (289 x^3-34 x^4+x^5\right ) \log ^4\left (x^2\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\log \left (x^2\right ) \left (-4 \log ^2(5)+2 \log ^2(5) \log \left (x^2\right )+(-34+3 x) \log ^3\left (x^2\right )\right )}{x^3 \left (\log ^2(5)+(-17+x) \log ^2\left (x^2\right )\right )^2} \, dx \\ & = \int \left (\frac {-34+3 x}{(-17+x)^2 x^3}-\frac {\log ^2(5) \left (-x \log ^2(5)+1156 \log \left (x^2\right )-136 x \log \left (x^2\right )+4 x^2 \log \left (x^2\right )\right )}{(-17+x)^2 x^3 \left (\log ^2(5)-17 \log ^2\left (x^2\right )+x \log ^2\left (x^2\right )\right )^2}-\frac {2 (-17+2 x) \log ^2(5)}{(-17+x)^2 x^3 \left (\log ^2(5)-17 \log ^2\left (x^2\right )+x \log ^2\left (x^2\right )\right )}\right ) \, dx \\ & = -\left (\log ^2(5) \int \frac {-x \log ^2(5)+1156 \log \left (x^2\right )-136 x \log \left (x^2\right )+4 x^2 \log \left (x^2\right )}{(-17+x)^2 x^3 \left (\log ^2(5)-17 \log ^2\left (x^2\right )+x \log ^2\left (x^2\right )\right )^2} \, dx\right )-\left (2 \log ^2(5)\right ) \int \frac {-17+2 x}{(-17+x)^2 x^3 \left (\log ^2(5)-17 \log ^2\left (x^2\right )+x \log ^2\left (x^2\right )\right )} \, dx+\int \frac {-34+3 x}{(-17+x)^2 x^3} \, dx \\ & = \frac {1}{(17-x) x^2}-\log ^2(5) \int \frac {-x \log ^2(5)+4 (-17+x)^2 \log \left (x^2\right )}{(17-x)^2 x^3 \left (\log ^2(5)+(-17+x) \log ^2\left (x^2\right )\right )^2} \, dx-\left (2 \log ^2(5)\right ) \int \left (\frac {1}{289 (-17+x)^2 \left (\log ^2(5)-17 \log ^2\left (x^2\right )+x \log ^2\left (x^2\right )\right )}-\frac {1}{4913 (-17+x) \left (\log ^2(5)-17 \log ^2\left (x^2\right )+x \log ^2\left (x^2\right )\right )}-\frac {1}{17 x^3 \left (\log ^2(5)-17 \log ^2\left (x^2\right )+x \log ^2\left (x^2\right )\right )}+\frac {1}{4913 x \left (\log ^2(5)-17 \log ^2\left (x^2\right )+x \log ^2\left (x^2\right )\right )}\right ) \, dx \\ & = \frac {1}{(17-x) x^2}+\frac {\left (2 \log ^2(5)\right ) \int \frac {1}{(-17+x) \left (\log ^2(5)-17 \log ^2\left (x^2\right )+x \log ^2\left (x^2\right )\right )} \, dx}{4913}-\frac {\left (2 \log ^2(5)\right ) \int \frac {1}{x \left (\log ^2(5)-17 \log ^2\left (x^2\right )+x \log ^2\left (x^2\right )\right )} \, dx}{4913}-\frac {1}{289} \left (2 \log ^2(5)\right ) \int \frac {1}{(-17+x)^2 \left (\log ^2(5)-17 \log ^2\left (x^2\right )+x \log ^2\left (x^2\right )\right )} \, dx+\frac {1}{17} \left (2 \log ^2(5)\right ) \int \frac {1}{x^3 \left (\log ^2(5)-17 \log ^2\left (x^2\right )+x \log ^2\left (x^2\right )\right )} \, dx-\log ^2(5) \int \left (\frac {-x \log ^2(5)+1156 \log \left (x^2\right )-136 x \log \left (x^2\right )+4 x^2 \log \left (x^2\right )}{4913 (-17+x)^2 \left (\log ^2(5)-17 \log ^2\left (x^2\right )+x \log ^2\left (x^2\right )\right )^2}-\frac {3 \left (-x \log ^2(5)+1156 \log \left (x^2\right )-136 x \log \left (x^2\right )+4 x^2 \log \left (x^2\right )\right )}{83521 (-17+x) \left (\log ^2(5)-17 \log ^2\left (x^2\right )+x \log ^2\left (x^2\right )\right )^2}+\frac {-x \log ^2(5)+1156 \log \left (x^2\right )-136 x \log \left (x^2\right )+4 x^2 \log \left (x^2\right )}{289 x^3 \left (\log ^2(5)-17 \log ^2\left (x^2\right )+x \log ^2\left (x^2\right )\right )^2}+\frac {2 \left (-x \log ^2(5)+1156 \log \left (x^2\right )-136 x \log \left (x^2\right )+4 x^2 \log \left (x^2\right )\right )}{4913 x^2 \left (\log ^2(5)-17 \log ^2\left (x^2\right )+x \log ^2\left (x^2\right )\right )^2}+\frac {3 \left (-x \log ^2(5)+1156 \log \left (x^2\right )-136 x \log \left (x^2\right )+4 x^2 \log \left (x^2\right )\right )}{83521 x \left (\log ^2(5)-17 \log ^2\left (x^2\right )+x \log ^2\left (x^2\right )\right )^2}\right ) \, dx \\ & = \frac {1}{(17-x) x^2}+\frac {\left (3 \log ^2(5)\right ) \int \frac {-x \log ^2(5)+1156 \log \left (x^2\right )-136 x \log \left (x^2\right )+4 x^2 \log \left (x^2\right )}{(-17+x) \left (\log ^2(5)-17 \log ^2\left (x^2\right )+x \log ^2\left (x^2\right )\right )^2} \, dx}{83521}-\frac {\left (3 \log ^2(5)\right ) \int \frac {-x \log ^2(5)+1156 \log \left (x^2\right )-136 x \log \left (x^2\right )+4 x^2 \log \left (x^2\right )}{x \left (\log ^2(5)-17 \log ^2\left (x^2\right )+x \log ^2\left (x^2\right )\right )^2} \, dx}{83521}-\frac {\log ^2(5) \int \frac {-x \log ^2(5)+1156 \log \left (x^2\right )-136 x \log \left (x^2\right )+4 x^2 \log \left (x^2\right )}{(-17+x)^2 \left (\log ^2(5)-17 \log ^2\left (x^2\right )+x \log ^2\left (x^2\right )\right )^2} \, dx}{4913}+\frac {\left (2 \log ^2(5)\right ) \int \frac {1}{(-17+x) \left (\log ^2(5)+(-17+x) \log ^2\left (x^2\right )\right )} \, dx}{4913}-\frac {\left (2 \log ^2(5)\right ) \int \frac {1}{x \left (\log ^2(5)+(-17+x) \log ^2\left (x^2\right )\right )} \, dx}{4913}-\frac {\left (2 \log ^2(5)\right ) \int \frac {-x \log ^2(5)+1156 \log \left (x^2\right )-136 x \log \left (x^2\right )+4 x^2 \log \left (x^2\right )}{x^2 \left (\log ^2(5)-17 \log ^2\left (x^2\right )+x \log ^2\left (x^2\right )\right )^2} \, dx}{4913}-\frac {1}{289} \log ^2(5) \int \frac {-x \log ^2(5)+1156 \log \left (x^2\right )-136 x \log \left (x^2\right )+4 x^2 \log \left (x^2\right )}{x^3 \left (\log ^2(5)-17 \log ^2\left (x^2\right )+x \log ^2\left (x^2\right )\right )^2} \, dx-\frac {1}{289} \left (2 \log ^2(5)\right ) \int \frac {1}{(-17+x)^2 \left (\log ^2(5)-17 \log ^2\left (x^2\right )+x \log ^2\left (x^2\right )\right )} \, dx+\frac {1}{17} \left (2 \log ^2(5)\right ) \int \frac {1}{x^3 \left (\log ^2(5)+(-17+x) \log ^2\left (x^2\right )\right )} \, dx \\ & = \frac {1}{(17-x) x^2}+\frac {\left (3 \log ^2(5)\right ) \int \frac {x \log ^2(5)-4 (-17+x)^2 \log \left (x^2\right )}{(17-x) \left (\log ^2(5)+(-17+x) \log ^2\left (x^2\right )\right )^2} \, dx}{83521}-\frac {\left (3 \log ^2(5)\right ) \int \frac {-x \log ^2(5)+4 (-17+x)^2 \log \left (x^2\right )}{x \left (\log ^2(5)+(-17+x) \log ^2\left (x^2\right )\right )^2} \, dx}{83521}-\frac {\log ^2(5) \int \frac {-x \log ^2(5)+4 (-17+x)^2 \log \left (x^2\right )}{(17-x)^2 \left (\log ^2(5)+(-17+x) \log ^2\left (x^2\right )\right )^2} \, dx}{4913}-\frac {\left (2 \log ^2(5)\right ) \int \frac {-x \log ^2(5)+4 (-17+x)^2 \log \left (x^2\right )}{x^2 \left (\log ^2(5)+(-17+x) \log ^2\left (x^2\right )\right )^2} \, dx}{4913}+\frac {\left (2 \log ^2(5)\right ) \int \frac {1}{(-17+x) \left (\log ^2(5)+(-17+x) \log ^2\left (x^2\right )\right )} \, dx}{4913}-\frac {\left (2 \log ^2(5)\right ) \int \frac {1}{x \left (\log ^2(5)+(-17+x) \log ^2\left (x^2\right )\right )} \, dx}{4913}-\frac {1}{289} \log ^2(5) \int \frac {-x \log ^2(5)+4 (-17+x)^2 \log \left (x^2\right )}{x^3 \left (\log ^2(5)+(-17+x) \log ^2\left (x^2\right )\right )^2} \, dx-\frac {1}{289} \left (2 \log ^2(5)\right ) \int \frac {1}{(-17+x)^2 \left (\log ^2(5)-17 \log ^2\left (x^2\right )+x \log ^2\left (x^2\right )\right )} \, dx+\frac {1}{17} \left (2 \log ^2(5)\right ) \int \frac {1}{x^3 \left (\log ^2(5)+(-17+x) \log ^2\left (x^2\right )\right )} \, dx \\ & = \text {Too large to display} \\ \end{align*}
Time = 0.55 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.22 \[ \int \frac {-4 \log ^2(5) \log \left (x^2\right )+2 \log ^2(5) \log ^2\left (x^2\right )+(-34+3 x) \log ^4\left (x^2\right )}{x^3 \log ^4(5)+\left (-34 x^3+2 x^4\right ) \log ^2(5) \log ^2\left (x^2\right )+\left (289 x^3-34 x^4+x^5\right ) \log ^4\left (x^2\right )} \, dx=-\frac {\log ^2\left (x^2\right )}{x^2 \left (\log ^2(5)+(-17+x) \log ^2\left (x^2\right )\right )} \]
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Time = 1.43 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.52
method | result | size |
parallelrisch | \(-\frac {\ln \left (x^{2}\right )^{2}}{x^{2} \left (x \ln \left (x^{2}\right )^{2}-17 \ln \left (x^{2}\right )^{2}+\ln \left (5\right )^{2}\right )}\) | \(35\) |
risch | \(-\frac {1}{x^{2} \left (x -17\right )}+\frac {\ln \left (5\right )^{2}}{x^{2} \left (x -17\right ) \left (x \ln \left (x^{2}\right )^{2}-17 \ln \left (x^{2}\right )^{2}+\ln \left (5\right )^{2}\right )}\) | \(48\) |
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Time = 0.29 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.52 \[ \int \frac {-4 \log ^2(5) \log \left (x^2\right )+2 \log ^2(5) \log ^2\left (x^2\right )+(-34+3 x) \log ^4\left (x^2\right )}{x^3 \log ^4(5)+\left (-34 x^3+2 x^4\right ) \log ^2(5) \log ^2\left (x^2\right )+\left (289 x^3-34 x^4+x^5\right ) \log ^4\left (x^2\right )} \, dx=-\frac {\log \left (x^{2}\right )^{2}}{x^{2} \log \left (5\right )^{2} + {\left (x^{3} - 17 \, x^{2}\right )} \log \left (x^{2}\right )^{2}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 53 vs. \(2 (19) = 38\).
Time = 0.13 (sec) , antiderivative size = 53, normalized size of antiderivative = 2.30 \[ \int \frac {-4 \log ^2(5) \log \left (x^2\right )+2 \log ^2(5) \log ^2\left (x^2\right )+(-34+3 x) \log ^4\left (x^2\right )}{x^3 \log ^4(5)+\left (-34 x^3+2 x^4\right ) \log ^2(5) \log ^2\left (x^2\right )+\left (289 x^3-34 x^4+x^5\right ) \log ^4\left (x^2\right )} \, dx=\frac {\log {\left (5 \right )}^{2}}{x^{3} \log {\left (5 \right )}^{2} - 17 x^{2} \log {\left (5 \right )}^{2} + \left (x^{4} - 34 x^{3} + 289 x^{2}\right ) \log {\left (x^{2} \right )}^{2}} - \frac {1}{x^{3} - 17 x^{2}} \]
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Time = 0.34 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.39 \[ \int \frac {-4 \log ^2(5) \log \left (x^2\right )+2 \log ^2(5) \log ^2\left (x^2\right )+(-34+3 x) \log ^4\left (x^2\right )}{x^3 \log ^4(5)+\left (-34 x^3+2 x^4\right ) \log ^2(5) \log ^2\left (x^2\right )+\left (289 x^3-34 x^4+x^5\right ) \log ^4\left (x^2\right )} \, dx=-\frac {4 \, \log \left (x\right )^{2}}{x^{2} \log \left (5\right )^{2} + 4 \, {\left (x^{3} - 17 \, x^{2}\right )} \log \left (x\right )^{2}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 73 vs. \(2 (21) = 42\).
Time = 0.40 (sec) , antiderivative size = 73, normalized size of antiderivative = 3.17 \[ \int \frac {-4 \log ^2(5) \log \left (x^2\right )+2 \log ^2(5) \log ^2\left (x^2\right )+(-34+3 x) \log ^4\left (x^2\right )}{x^3 \log ^4(5)+\left (-34 x^3+2 x^4\right ) \log ^2(5) \log ^2\left (x^2\right )+\left (289 x^3-34 x^4+x^5\right ) \log ^4\left (x^2\right )} \, dx=\frac {\log \left (5\right )^{2}}{x^{4} \log \left (x^{2}\right )^{2} + x^{3} \log \left (5\right )^{2} - 34 \, x^{3} \log \left (x^{2}\right )^{2} - 17 \, x^{2} \log \left (5\right )^{2} + 289 \, x^{2} \log \left (x^{2}\right )^{2}} - \frac {1}{289 \, {\left (x - 17\right )}} + \frac {x + 17}{289 \, x^{2}} \]
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Time = 14.80 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.48 \[ \int \frac {-4 \log ^2(5) \log \left (x^2\right )+2 \log ^2(5) \log ^2\left (x^2\right )+(-34+3 x) \log ^4\left (x^2\right )}{x^3 \log ^4(5)+\left (-34 x^3+2 x^4\right ) \log ^2(5) \log ^2\left (x^2\right )+\left (289 x^3-34 x^4+x^5\right ) \log ^4\left (x^2\right )} \, dx=-\frac {{\ln \left (x^2\right )}^2}{x^2\,\left (x\,{\ln \left (x^2\right )}^2-17\,{\ln \left (x^2\right )}^2+{\ln \left (5\right )}^2\right )} \]
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