Integrand size = 351, antiderivative size = 21 \[ \int \frac {-2 x^2-2 x \log (x)+\left (-2 x-4 x^2-2 x \log (x)\right ) \log (25 x)+\left (2 x^2+2 x \log (x)\right ) \log (25 x) \log (x+\log (x))+\left (2 x^2+2 x \log (x)\right ) \log (25 x) \log (\log (25 x))}{\left (-x-3 x^2-3 x^3-x^4+\left (-1-3 x-3 x^2-x^3\right ) \log (x)\right ) \log (25 x)+\left (3 x+6 x^2+3 x^3+\left (3+6 x+3 x^2\right ) \log (x)\right ) \log (25 x) \log (x+\log (x))+\left (-3 x-3 x^2+(-3-3 x) \log (x)\right ) \log (25 x) \log ^2(x+\log (x))+(x+\log (x)) \log (25 x) \log ^3(x+\log (x))+\left (\left (3 x+6 x^2+3 x^3+\left (3+6 x+3 x^2\right ) \log (x)\right ) \log (25 x)+\left (-6 x-6 x^2+(-6-6 x) \log (x)\right ) \log (25 x) \log (x+\log (x))+(3 x+3 \log (x)) \log (25 x) \log ^2(x+\log (x))\right ) \log (\log (25 x))+\left (\left (-3 x-3 x^2+(-3-3 x) \log (x)\right ) \log (25 x)+(3 x+3 \log (x)) \log (25 x) \log (x+\log (x))\right ) \log ^2(\log (25 x))+(x+\log (x)) \log (25 x) \log ^3(\log (25 x))} \, dx=\frac {x^2}{(-1-x+\log (x+\log (x))+\log (\log (25 x)))^2} \]
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\[ \int \frac {-2 x^2-2 x \log (x)+\left (-2 x-4 x^2-2 x \log (x)\right ) \log (25 x)+\left (2 x^2+2 x \log (x)\right ) \log (25 x) \log (x+\log (x))+\left (2 x^2+2 x \log (x)\right ) \log (25 x) \log (\log (25 x))}{\left (-x-3 x^2-3 x^3-x^4+\left (-1-3 x-3 x^2-x^3\right ) \log (x)\right ) \log (25 x)+\left (3 x+6 x^2+3 x^3+\left (3+6 x+3 x^2\right ) \log (x)\right ) \log (25 x) \log (x+\log (x))+\left (-3 x-3 x^2+(-3-3 x) \log (x)\right ) \log (25 x) \log ^2(x+\log (x))+(x+\log (x)) \log (25 x) \log ^3(x+\log (x))+\left (\left (3 x+6 x^2+3 x^3+\left (3+6 x+3 x^2\right ) \log (x)\right ) \log (25 x)+\left (-6 x-6 x^2+(-6-6 x) \log (x)\right ) \log (25 x) \log (x+\log (x))+(3 x+3 \log (x)) \log (25 x) \log ^2(x+\log (x))\right ) \log (\log (25 x))+\left (\left (-3 x-3 x^2+(-3-3 x) \log (x)\right ) \log (25 x)+(3 x+3 \log (x)) \log (25 x) \log (x+\log (x))\right ) \log ^2(\log (25 x))+(x+\log (x)) \log (25 x) \log ^3(\log (25 x))} \, dx=\int \frac {-2 x^2-2 x \log (x)+\left (-2 x-4 x^2-2 x \log (x)\right ) \log (25 x)+\left (2 x^2+2 x \log (x)\right ) \log (25 x) \log (x+\log (x))+\left (2 x^2+2 x \log (x)\right ) \log (25 x) \log (\log (25 x))}{\left (-x-3 x^2-3 x^3-x^4+\left (-1-3 x-3 x^2-x^3\right ) \log (x)\right ) \log (25 x)+\left (3 x+6 x^2+3 x^3+\left (3+6 x+3 x^2\right ) \log (x)\right ) \log (25 x) \log (x+\log (x))+\left (-3 x-3 x^2+(-3-3 x) \log (x)\right ) \log (25 x) \log ^2(x+\log (x))+(x+\log (x)) \log (25 x) \log ^3(x+\log (x))+\left (\left (3 x+6 x^2+3 x^3+\left (3+6 x+3 x^2\right ) \log (x)\right ) \log (25 x)+\left (-6 x-6 x^2+(-6-6 x) \log (x)\right ) \log (25 x) \log (x+\log (x))+(3 x+3 \log (x)) \log (25 x) \log ^2(x+\log (x))\right ) \log (\log (25 x))+\left (\left (-3 x-3 x^2+(-3-3 x) \log (x)\right ) \log (25 x)+(3 x+3 \log (x)) \log (25 x) \log (x+\log (x))\right ) \log ^2(\log (25 x))+(x+\log (x)) \log (25 x) \log ^3(\log (25 x))} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {2 x (x-\log (25 x) (-1-2 x+x \log (x+\log (x))+x \log (\log (25 x)))-\log (x) (-1+\log (25 x) (-1+\log (x+\log (x))+\log (\log (25 x)))))}{(x+\log (x)) \log (25 x) (1+x-\log (x+\log (x))-\log (\log (25 x)))^3} \, dx \\ & = 2 \int \frac {x (x-\log (25 x) (-1-2 x+x \log (x+\log (x))+x \log (\log (25 x)))-\log (x) (-1+\log (25 x) (-1+\log (x+\log (x))+\log (\log (25 x)))))}{(x+\log (x)) \log (25 x) (1+x-\log (x+\log (x))-\log (\log (25 x)))^3} \, dx \\ & = 2 \int \left (-\frac {x \left (-x-\log (x)-\log (25 x)-x \log (25 x)+x^2 \log (25 x)+x \log (x) \log (25 x)\right )}{(x+\log (x)) \log (25 x) (1+x-\log (x+\log (x))-\log (\log (25 x)))^3}+\frac {x}{(1+x-\log (x+\log (x))-\log (\log (25 x)))^2}\right ) \, dx \\ & = -\left (2 \int \frac {x \left (-x-\log (x)-\log (25 x)-x \log (25 x)+x^2 \log (25 x)+x \log (x) \log (25 x)\right )}{(x+\log (x)) \log (25 x) (1+x-\log (x+\log (x))-\log (\log (25 x)))^3} \, dx\right )+2 \int \frac {x}{(1+x-\log (x+\log (x))-\log (\log (25 x)))^2} \, dx \\ & = -\left (2 \int \left (-\frac {x}{(x+\log (x)) (1+x-\log (x+\log (x))-\log (\log (25 x)))^3}-\frac {x^2}{(x+\log (x)) (1+x-\log (x+\log (x))-\log (\log (25 x)))^3}+\frac {x^3}{(x+\log (x)) (1+x-\log (x+\log (x))-\log (\log (25 x)))^3}+\frac {x^2 \log (x)}{(x+\log (x)) (1+x-\log (x+\log (x))-\log (\log (25 x)))^3}-\frac {x^2}{(x+\log (x)) \log (25 x) (1+x-\log (x+\log (x))-\log (\log (25 x)))^3}-\frac {x \log (x)}{(x+\log (x)) \log (25 x) (1+x-\log (x+\log (x))-\log (\log (25 x)))^3}\right ) \, dx\right )+2 \int \frac {x}{(1+x-\log (x+\log (x))-\log (\log (25 x)))^2} \, dx \\ & = 2 \int \frac {x}{(x+\log (x)) (1+x-\log (x+\log (x))-\log (\log (25 x)))^3} \, dx+2 \int \frac {x^2}{(x+\log (x)) (1+x-\log (x+\log (x))-\log (\log (25 x)))^3} \, dx-2 \int \frac {x^3}{(x+\log (x)) (1+x-\log (x+\log (x))-\log (\log (25 x)))^3} \, dx-2 \int \frac {x^2 \log (x)}{(x+\log (x)) (1+x-\log (x+\log (x))-\log (\log (25 x)))^3} \, dx+2 \int \frac {x^2}{(x+\log (x)) \log (25 x) (1+x-\log (x+\log (x))-\log (\log (25 x)))^3} \, dx+2 \int \frac {x \log (x)}{(x+\log (x)) \log (25 x) (1+x-\log (x+\log (x))-\log (\log (25 x)))^3} \, dx+2 \int \frac {x}{(1+x-\log (x+\log (x))-\log (\log (25 x)))^2} \, dx \\ \end{align*}
Time = 0.11 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.00 \[ \int \frac {-2 x^2-2 x \log (x)+\left (-2 x-4 x^2-2 x \log (x)\right ) \log (25 x)+\left (2 x^2+2 x \log (x)\right ) \log (25 x) \log (x+\log (x))+\left (2 x^2+2 x \log (x)\right ) \log (25 x) \log (\log (25 x))}{\left (-x-3 x^2-3 x^3-x^4+\left (-1-3 x-3 x^2-x^3\right ) \log (x)\right ) \log (25 x)+\left (3 x+6 x^2+3 x^3+\left (3+6 x+3 x^2\right ) \log (x)\right ) \log (25 x) \log (x+\log (x))+\left (-3 x-3 x^2+(-3-3 x) \log (x)\right ) \log (25 x) \log ^2(x+\log (x))+(x+\log (x)) \log (25 x) \log ^3(x+\log (x))+\left (\left (3 x+6 x^2+3 x^3+\left (3+6 x+3 x^2\right ) \log (x)\right ) \log (25 x)+\left (-6 x-6 x^2+(-6-6 x) \log (x)\right ) \log (25 x) \log (x+\log (x))+(3 x+3 \log (x)) \log (25 x) \log ^2(x+\log (x))\right ) \log (\log (25 x))+\left (\left (-3 x-3 x^2+(-3-3 x) \log (x)\right ) \log (25 x)+(3 x+3 \log (x)) \log (25 x) \log (x+\log (x))\right ) \log ^2(\log (25 x))+(x+\log (x)) \log (25 x) \log ^3(\log (25 x))} \, dx=\frac {x^2}{(-1-x+\log (x+\log (x))+\log (\log (25 x)))^2} \]
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Time = 270.14 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.29
method | result | size |
default | \(\frac {x^{2}}{\left (x -\ln \left (2 \ln \left (5\right )+\ln \left (x \right )\right )-\ln \left (x +\ln \left (x \right )\right )+1\right )^{2}}\) | \(27\) |
risch | \(\frac {x^{2}}{\left (x -\ln \left (2 \ln \left (5\right )+\ln \left (x \right )\right )-\ln \left (x +\ln \left (x \right )\right )+1\right )^{2}}\) | \(27\) |
parallelrisch | \(\frac {x^{2}}{x^{2}-2 \ln \left (\ln \left (25 x \right )\right ) x -2 \ln \left (x +\ln \left (x \right )\right ) x +\ln \left (\ln \left (25 x \right )\right )^{2}+2 \ln \left (\ln \left (25 x \right )\right ) \ln \left (x +\ln \left (x \right )\right )+\ln \left (x +\ln \left (x \right )\right )^{2}+2 x -2 \ln \left (\ln \left (25 x \right )\right )-2 \ln \left (x +\ln \left (x \right )\right )+1}\) | \(71\) |
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Leaf count of result is larger than twice the leaf count of optimal. 61 vs. \(2 (23) = 46\).
Time = 0.26 (sec) , antiderivative size = 61, normalized size of antiderivative = 2.90 \[ \int \frac {-2 x^2-2 x \log (x)+\left (-2 x-4 x^2-2 x \log (x)\right ) \log (25 x)+\left (2 x^2+2 x \log (x)\right ) \log (25 x) \log (x+\log (x))+\left (2 x^2+2 x \log (x)\right ) \log (25 x) \log (\log (25 x))}{\left (-x-3 x^2-3 x^3-x^4+\left (-1-3 x-3 x^2-x^3\right ) \log (x)\right ) \log (25 x)+\left (3 x+6 x^2+3 x^3+\left (3+6 x+3 x^2\right ) \log (x)\right ) \log (25 x) \log (x+\log (x))+\left (-3 x-3 x^2+(-3-3 x) \log (x)\right ) \log (25 x) \log ^2(x+\log (x))+(x+\log (x)) \log (25 x) \log ^3(x+\log (x))+\left (\left (3 x+6 x^2+3 x^3+\left (3+6 x+3 x^2\right ) \log (x)\right ) \log (25 x)+\left (-6 x-6 x^2+(-6-6 x) \log (x)\right ) \log (25 x) \log (x+\log (x))+(3 x+3 \log (x)) \log (25 x) \log ^2(x+\log (x))\right ) \log (\log (25 x))+\left (\left (-3 x-3 x^2+(-3-3 x) \log (x)\right ) \log (25 x)+(3 x+3 \log (x)) \log (25 x) \log (x+\log (x))\right ) \log ^2(\log (25 x))+(x+\log (x)) \log (25 x) \log ^3(\log (25 x))} \, dx=\frac {x^{2}}{x^{2} - 2 \, {\left (x + 1\right )} \log \left (x + \log \left (x\right )\right ) + \log \left (x + \log \left (x\right )\right )^{2} - 2 \, {\left (x - \log \left (x + \log \left (x\right )\right ) + 1\right )} \log \left (2 \, \log \left (5\right ) + \log \left (x\right )\right ) + \log \left (2 \, \log \left (5\right ) + \log \left (x\right )\right )^{2} + 2 \, x + 1} \]
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Leaf count of result is larger than twice the leaf count of optimal. 70 vs. \(2 (20) = 40\).
Time = 0.55 (sec) , antiderivative size = 70, normalized size of antiderivative = 3.33 \[ \int \frac {-2 x^2-2 x \log (x)+\left (-2 x-4 x^2-2 x \log (x)\right ) \log (25 x)+\left (2 x^2+2 x \log (x)\right ) \log (25 x) \log (x+\log (x))+\left (2 x^2+2 x \log (x)\right ) \log (25 x) \log (\log (25 x))}{\left (-x-3 x^2-3 x^3-x^4+\left (-1-3 x-3 x^2-x^3\right ) \log (x)\right ) \log (25 x)+\left (3 x+6 x^2+3 x^3+\left (3+6 x+3 x^2\right ) \log (x)\right ) \log (25 x) \log (x+\log (x))+\left (-3 x-3 x^2+(-3-3 x) \log (x)\right ) \log (25 x) \log ^2(x+\log (x))+(x+\log (x)) \log (25 x) \log ^3(x+\log (x))+\left (\left (3 x+6 x^2+3 x^3+\left (3+6 x+3 x^2\right ) \log (x)\right ) \log (25 x)+\left (-6 x-6 x^2+(-6-6 x) \log (x)\right ) \log (25 x) \log (x+\log (x))+(3 x+3 \log (x)) \log (25 x) \log ^2(x+\log (x))\right ) \log (\log (25 x))+\left (\left (-3 x-3 x^2+(-3-3 x) \log (x)\right ) \log (25 x)+(3 x+3 \log (x)) \log (25 x) \log (x+\log (x))\right ) \log ^2(\log (25 x))+(x+\log (x)) \log (25 x) \log ^3(\log (25 x))} \, dx=\frac {x^{2}}{x^{2} - 2 x \log {\left (x + \log {\left (x \right )} \right )} + 2 x + \left (- 2 x + 2 \log {\left (x + \log {\left (x \right )} \right )} - 2\right ) \log {\left (\log {\left (x \right )} + \log {\left (25 \right )} \right )} + \log {\left (x + \log {\left (x \right )} \right )}^{2} - 2 \log {\left (x + \log {\left (x \right )} \right )} + \log {\left (\log {\left (x \right )} + \log {\left (25 \right )} \right )}^{2} + 1} \]
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Leaf count of result is larger than twice the leaf count of optimal. 61 vs. \(2 (23) = 46\).
Time = 0.48 (sec) , antiderivative size = 61, normalized size of antiderivative = 2.90 \[ \int \frac {-2 x^2-2 x \log (x)+\left (-2 x-4 x^2-2 x \log (x)\right ) \log (25 x)+\left (2 x^2+2 x \log (x)\right ) \log (25 x) \log (x+\log (x))+\left (2 x^2+2 x \log (x)\right ) \log (25 x) \log (\log (25 x))}{\left (-x-3 x^2-3 x^3-x^4+\left (-1-3 x-3 x^2-x^3\right ) \log (x)\right ) \log (25 x)+\left (3 x+6 x^2+3 x^3+\left (3+6 x+3 x^2\right ) \log (x)\right ) \log (25 x) \log (x+\log (x))+\left (-3 x-3 x^2+(-3-3 x) \log (x)\right ) \log (25 x) \log ^2(x+\log (x))+(x+\log (x)) \log (25 x) \log ^3(x+\log (x))+\left (\left (3 x+6 x^2+3 x^3+\left (3+6 x+3 x^2\right ) \log (x)\right ) \log (25 x)+\left (-6 x-6 x^2+(-6-6 x) \log (x)\right ) \log (25 x) \log (x+\log (x))+(3 x+3 \log (x)) \log (25 x) \log ^2(x+\log (x))\right ) \log (\log (25 x))+\left (\left (-3 x-3 x^2+(-3-3 x) \log (x)\right ) \log (25 x)+(3 x+3 \log (x)) \log (25 x) \log (x+\log (x))\right ) \log ^2(\log (25 x))+(x+\log (x)) \log (25 x) \log ^3(\log (25 x))} \, dx=\frac {x^{2}}{x^{2} - 2 \, {\left (x + 1\right )} \log \left (x + \log \left (x\right )\right ) + \log \left (x + \log \left (x\right )\right )^{2} - 2 \, {\left (x - \log \left (x + \log \left (x\right )\right ) + 1\right )} \log \left (2 \, \log \left (5\right ) + \log \left (x\right )\right ) + \log \left (2 \, \log \left (5\right ) + \log \left (x\right )\right )^{2} + 2 \, x + 1} \]
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Leaf count of result is larger than twice the leaf count of optimal. 900 vs. \(2 (23) = 46\).
Time = 0.69 (sec) , antiderivative size = 900, normalized size of antiderivative = 42.86 \[ \int \frac {-2 x^2-2 x \log (x)+\left (-2 x-4 x^2-2 x \log (x)\right ) \log (25 x)+\left (2 x^2+2 x \log (x)\right ) \log (25 x) \log (x+\log (x))+\left (2 x^2+2 x \log (x)\right ) \log (25 x) \log (\log (25 x))}{\left (-x-3 x^2-3 x^3-x^4+\left (-1-3 x-3 x^2-x^3\right ) \log (x)\right ) \log (25 x)+\left (3 x+6 x^2+3 x^3+\left (3+6 x+3 x^2\right ) \log (x)\right ) \log (25 x) \log (x+\log (x))+\left (-3 x-3 x^2+(-3-3 x) \log (x)\right ) \log (25 x) \log ^2(x+\log (x))+(x+\log (x)) \log (25 x) \log ^3(x+\log (x))+\left (\left (3 x+6 x^2+3 x^3+\left (3+6 x+3 x^2\right ) \log (x)\right ) \log (25 x)+\left (-6 x-6 x^2+(-6-6 x) \log (x)\right ) \log (25 x) \log (x+\log (x))+(3 x+3 \log (x)) \log (25 x) \log ^2(x+\log (x))\right ) \log (\log (25 x))+\left (\left (-3 x-3 x^2+(-3-3 x) \log (x)\right ) \log (25 x)+(3 x+3 \log (x)) \log (25 x) \log (x+\log (x))\right ) \log ^2(\log (25 x))+(x+\log (x)) \log (25 x) \log ^3(\log (25 x))} \, dx=\text {Too large to display} \]
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Timed out. \[ \int \frac {-2 x^2-2 x \log (x)+\left (-2 x-4 x^2-2 x \log (x)\right ) \log (25 x)+\left (2 x^2+2 x \log (x)\right ) \log (25 x) \log (x+\log (x))+\left (2 x^2+2 x \log (x)\right ) \log (25 x) \log (\log (25 x))}{\left (-x-3 x^2-3 x^3-x^4+\left (-1-3 x-3 x^2-x^3\right ) \log (x)\right ) \log (25 x)+\left (3 x+6 x^2+3 x^3+\left (3+6 x+3 x^2\right ) \log (x)\right ) \log (25 x) \log (x+\log (x))+\left (-3 x-3 x^2+(-3-3 x) \log (x)\right ) \log (25 x) \log ^2(x+\log (x))+(x+\log (x)) \log (25 x) \log ^3(x+\log (x))+\left (\left (3 x+6 x^2+3 x^3+\left (3+6 x+3 x^2\right ) \log (x)\right ) \log (25 x)+\left (-6 x-6 x^2+(-6-6 x) \log (x)\right ) \log (25 x) \log (x+\log (x))+(3 x+3 \log (x)) \log (25 x) \log ^2(x+\log (x))\right ) \log (\log (25 x))+\left (\left (-3 x-3 x^2+(-3-3 x) \log (x)\right ) \log (25 x)+(3 x+3 \log (x)) \log (25 x) \log (x+\log (x))\right ) \log ^2(\log (25 x))+(x+\log (x)) \log (25 x) \log ^3(\log (25 x))} \, dx=\int -\frac {2\,x\,\ln \left (x\right )+\ln \left (25\,x\right )\,\left (2\,x+2\,x\,\ln \left (x\right )+4\,x^2\right )+2\,x^2-\ln \left (x+\ln \left (x\right )\right )\,\ln \left (25\,x\right )\,\left (2\,x\,\ln \left (x\right )+2\,x^2\right )-\ln \left (25\,x\right )\,\ln \left (\ln \left (25\,x\right )\right )\,\left (2\,x\,\ln \left (x\right )+2\,x^2\right )}{\ln \left (\ln \left (25\,x\right )\right )\,\left (\ln \left (25\,x\right )\,\left (3\,x+3\,\ln \left (x\right )\right )\,{\ln \left (x+\ln \left (x\right )\right )}^2-\ln \left (25\,x\right )\,\left (6\,x+\ln \left (x\right )\,\left (6\,x+6\right )+6\,x^2\right )\,\ln \left (x+\ln \left (x\right )\right )+\ln \left (25\,x\right )\,\left (3\,x+\ln \left (x\right )\,\left (3\,x^2+6\,x+3\right )+6\,x^2+3\,x^3\right )\right )-{\ln \left (\ln \left (25\,x\right )\right )}^2\,\left (\ln \left (25\,x\right )\,\left (3\,x+\ln \left (x\right )\,\left (3\,x+3\right )+3\,x^2\right )-\ln \left (x+\ln \left (x\right )\right )\,\ln \left (25\,x\right )\,\left (3\,x+3\,\ln \left (x\right )\right )\right )-\ln \left (25\,x\right )\,\left (x+\ln \left (x\right )\,\left (x^3+3\,x^2+3\,x+1\right )+3\,x^2+3\,x^3+x^4\right )-{\ln \left (x+\ln \left (x\right )\right )}^2\,\ln \left (25\,x\right )\,\left (3\,x+\ln \left (x\right )\,\left (3\,x+3\right )+3\,x^2\right )+\ln \left (x+\ln \left (x\right )\right )\,\ln \left (25\,x\right )\,\left (3\,x+\ln \left (x\right )\,\left (3\,x^2+6\,x+3\right )+6\,x^2+3\,x^3\right )+\ln \left (25\,x\right )\,{\ln \left (\ln \left (25\,x\right )\right )}^3\,\left (x+\ln \left (x\right )\right )+{\ln \left (x+\ln \left (x\right )\right )}^3\,\ln \left (25\,x\right )\,\left (x+\ln \left (x\right )\right )} \,d x \]
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