Integrand size = 517, antiderivative size = 30 \[ \int \frac {-12-9 x+3 x^2+e^4 \left (3 x+3 x^2\right )+e^2 \left (-6 x+6 x^2\right )+\left (6 x-6 x^2+e^2 \left (-6 x-6 x^2\right )\right ) \log (x)+\left (3 x+3 x^2\right ) \log ^2(x)}{20 x^3-5 x^4-5 e^4 x^4+e^2 \left (20 x^3-10 x^4\right )+\left (-4 x^3+x^4+e^4 x^4+e^2 \left (-4 x^3+2 x^4\right )\right ) \log (3)+\left (-20 x^3+10 x^4+10 e^2 x^4+\left (4 x^3-2 x^4-2 e^2 x^4\right ) \log (3)\right ) \log (x)+\left (-5 x^4+x^4 \log (3)\right ) \log ^2(x)+\left (40 x^2-10 x^3-10 e^4 x^3+e^2 \left (40 x^2-20 x^3\right )+\left (-8 x^2+2 x^3+2 e^4 x^3+e^2 \left (-8 x^2+4 x^3\right )\right ) \log (3)+\left (-40 x^2+20 x^3+20 e^2 x^3+\left (8 x^2-4 x^3-4 e^2 x^3\right ) \log (3)\right ) \log (x)+\left (-10 x^3+2 x^3 \log (3)\right ) \log ^2(x)\right ) \log \left (\frac {4-x-e^2 x+x \log (x)}{-1-e^2+\log (x)}\right )+\left (20 x-5 x^2-5 e^4 x^2+e^2 \left (20 x-10 x^2\right )+\left (-4 x+x^2+e^4 x^2+e^2 \left (-4 x+2 x^2\right )\right ) \log (3)+\left (-20 x+10 x^2+10 e^2 x^2+\left (4 x-2 x^2-2 e^2 x^2\right ) \log (3)\right ) \log (x)+\left (-5 x^2+x^2 \log (3)\right ) \log ^2(x)\right ) \log ^2\left (\frac {4-x-e^2 x+x \log (x)}{-1-e^2+\log (x)}\right )} \, dx=\frac {3}{(5-\log (3)) \left (x+\log \left (x-\frac {4}{1+e^2-\log (x)}\right )\right )} \]
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\[ \int \frac {-12-9 x+3 x^2+e^4 \left (3 x+3 x^2\right )+e^2 \left (-6 x+6 x^2\right )+\left (6 x-6 x^2+e^2 \left (-6 x-6 x^2\right )\right ) \log (x)+\left (3 x+3 x^2\right ) \log ^2(x)}{20 x^3-5 x^4-5 e^4 x^4+e^2 \left (20 x^3-10 x^4\right )+\left (-4 x^3+x^4+e^4 x^4+e^2 \left (-4 x^3+2 x^4\right )\right ) \log (3)+\left (-20 x^3+10 x^4+10 e^2 x^4+\left (4 x^3-2 x^4-2 e^2 x^4\right ) \log (3)\right ) \log (x)+\left (-5 x^4+x^4 \log (3)\right ) \log ^2(x)+\left (40 x^2-10 x^3-10 e^4 x^3+e^2 \left (40 x^2-20 x^3\right )+\left (-8 x^2+2 x^3+2 e^4 x^3+e^2 \left (-8 x^2+4 x^3\right )\right ) \log (3)+\left (-40 x^2+20 x^3+20 e^2 x^3+\left (8 x^2-4 x^3-4 e^2 x^3\right ) \log (3)\right ) \log (x)+\left (-10 x^3+2 x^3 \log (3)\right ) \log ^2(x)\right ) \log \left (\frac {4-x-e^2 x+x \log (x)}{-1-e^2+\log (x)}\right )+\left (20 x-5 x^2-5 e^4 x^2+e^2 \left (20 x-10 x^2\right )+\left (-4 x+x^2+e^4 x^2+e^2 \left (-4 x+2 x^2\right )\right ) \log (3)+\left (-20 x+10 x^2+10 e^2 x^2+\left (4 x-2 x^2-2 e^2 x^2\right ) \log (3)\right ) \log (x)+\left (-5 x^2+x^2 \log (3)\right ) \log ^2(x)\right ) \log ^2\left (\frac {4-x-e^2 x+x \log (x)}{-1-e^2+\log (x)}\right )} \, dx=\int \frac {-12-9 x+3 x^2+e^4 \left (3 x+3 x^2\right )+e^2 \left (-6 x+6 x^2\right )+\left (6 x-6 x^2+e^2 \left (-6 x-6 x^2\right )\right ) \log (x)+\left (3 x+3 x^2\right ) \log ^2(x)}{20 x^3-5 x^4-5 e^4 x^4+e^2 \left (20 x^3-10 x^4\right )+\left (-4 x^3+x^4+e^4 x^4+e^2 \left (-4 x^3+2 x^4\right )\right ) \log (3)+\left (-20 x^3+10 x^4+10 e^2 x^4+\left (4 x^3-2 x^4-2 e^2 x^4\right ) \log (3)\right ) \log (x)+\left (-5 x^4+x^4 \log (3)\right ) \log ^2(x)+\left (40 x^2-10 x^3-10 e^4 x^3+e^2 \left (40 x^2-20 x^3\right )+\left (-8 x^2+2 x^3+2 e^4 x^3+e^2 \left (-8 x^2+4 x^3\right )\right ) \log (3)+\left (-40 x^2+20 x^3+20 e^2 x^3+\left (8 x^2-4 x^3-4 e^2 x^3\right ) \log (3)\right ) \log (x)+\left (-10 x^3+2 x^3 \log (3)\right ) \log ^2(x)\right ) \log \left (\frac {4-x-e^2 x+x \log (x)}{-1-e^2+\log (x)}\right )+\left (20 x-5 x^2-5 e^4 x^2+e^2 \left (20 x-10 x^2\right )+\left (-4 x+x^2+e^4 x^2+e^2 \left (-4 x+2 x^2\right )\right ) \log (3)+\left (-20 x+10 x^2+10 e^2 x^2+\left (4 x-2 x^2-2 e^2 x^2\right ) \log (3)\right ) \log (x)+\left (-5 x^2+x^2 \log (3)\right ) \log ^2(x)\right ) \log ^2\left (\frac {4-x-e^2 x+x \log (x)}{-1-e^2+\log (x)}\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {-12-9 x+3 x^2+e^4 \left (3 x+3 x^2\right )+e^2 \left (-6 x+6 x^2\right )+\left (6 x-6 x^2+e^2 \left (-6 x-6 x^2\right )\right ) \log (x)+\left (3 x+3 x^2\right ) \log ^2(x)}{20 x^3+\left (-5-5 e^4\right ) x^4+e^2 \left (20 x^3-10 x^4\right )+\left (-4 x^3+x^4+e^4 x^4+e^2 \left (-4 x^3+2 x^4\right )\right ) \log (3)+\left (-20 x^3+10 x^4+10 e^2 x^4+\left (4 x^3-2 x^4-2 e^2 x^4\right ) \log (3)\right ) \log (x)+\left (-5 x^4+x^4 \log (3)\right ) \log ^2(x)+\left (40 x^2-10 x^3-10 e^4 x^3+e^2 \left (40 x^2-20 x^3\right )+\left (-8 x^2+2 x^3+2 e^4 x^3+e^2 \left (-8 x^2+4 x^3\right )\right ) \log (3)+\left (-40 x^2+20 x^3+20 e^2 x^3+\left (8 x^2-4 x^3-4 e^2 x^3\right ) \log (3)\right ) \log (x)+\left (-10 x^3+2 x^3 \log (3)\right ) \log ^2(x)\right ) \log \left (\frac {4-x-e^2 x+x \log (x)}{-1-e^2+\log (x)}\right )+\left (20 x-5 x^2-5 e^4 x^2+e^2 \left (20 x-10 x^2\right )+\left (-4 x+x^2+e^4 x^2+e^2 \left (-4 x+2 x^2\right )\right ) \log (3)+\left (-20 x+10 x^2+10 e^2 x^2+\left (4 x-2 x^2-2 e^2 x^2\right ) \log (3)\right ) \log (x)+\left (-5 x^2+x^2 \log (3)\right ) \log ^2(x)\right ) \log ^2\left (\frac {4-x-e^2 x+x \log (x)}{-1-e^2+\log (x)}\right )} \, dx \\ & = \int \frac {3 \left (-4+\left (-3-2 e^2+e^4\right ) x+\left (1+e^2\right )^2 x^2-2 x \left (-1+x+e^2 (1+x)\right ) \log (x)+x (1+x) \log ^2(x)\right )}{x (5-\log (3)) \left (1+e^2-\log (x)\right ) \left (4-\left (1+e^2\right ) x+x \log (x)\right ) \left (x+\log \left (\frac {-4+x+e^2 x-x \log (x)}{1+e^2-\log (x)}\right )\right )^2} \, dx \\ & = \frac {3 \int \frac {-4+\left (-3-2 e^2+e^4\right ) x+\left (1+e^2\right )^2 x^2-2 x \left (-1+x+e^2 (1+x)\right ) \log (x)+x (1+x) \log ^2(x)}{x \left (1+e^2-\log (x)\right ) \left (4-\left (1+e^2\right ) x+x \log (x)\right ) \left (x+\log \left (\frac {-4+x+e^2 x-x \log (x)}{1+e^2-\log (x)}\right )\right )^2} \, dx}{5-\log (3)} \\ & = \frac {3 \int \left (\frac {-3-2 e^2+e^4}{\left (1+e^2-\log (x)\right ) \left (4-\left (1+e^2\right ) x+x \log (x)\right ) \left (x+\log \left (\frac {-4+x+e^2 x-x \log (x)}{1+e^2-\log (x)}\right )\right )^2}+\frac {\left (1+e^2\right )^2 x}{\left (1+e^2-\log (x)\right ) \left (4-\left (1+e^2\right ) x+x \log (x)\right ) \left (x+\log \left (\frac {-4+x+e^2 x-x \log (x)}{1+e^2-\log (x)}\right )\right )^2}+\frac {2 \left (1-e^2\right ) \log (x)}{\left (1+e^2-\log (x)\right ) \left (4-\left (1+e^2\right ) x+x \log (x)\right ) \left (x+\log \left (\frac {-4+x+e^2 x-x \log (x)}{1+e^2-\log (x)}\right )\right )^2}+\frac {\log ^2(x)}{\left (1+e^2-\log (x)\right ) \left (4-\left (1+e^2\right ) x+x \log (x)\right ) \left (x+\log \left (\frac {-4+x+e^2 x-x \log (x)}{1+e^2-\log (x)}\right )\right )^2}+\frac {x \log ^2(x)}{\left (1+e^2-\log (x)\right ) \left (4-\left (1+e^2\right ) x+x \log (x)\right ) \left (x+\log \left (\frac {-4+x+e^2 x-x \log (x)}{1+e^2-\log (x)}\right )\right )^2}+\frac {4}{x \left (-1-e^2+\log (x)\right ) \left (4-\left (1+e^2\right ) x+x \log (x)\right ) \left (x+\log \left (\frac {-4+x+e^2 x-x \log (x)}{1+e^2-\log (x)}\right )\right )^2}+\frac {2 \left (1+e^2\right ) x \log (x)}{\left (-1-e^2+\log (x)\right ) \left (4-\left (1+e^2\right ) x+x \log (x)\right ) \left (x+\log \left (\frac {-4+x+e^2 x-x \log (x)}{1+e^2-\log (x)}\right )\right )^2}\right ) \, dx}{5-\log (3)} \\ & = \frac {3 \int \frac {\log ^2(x)}{\left (1+e^2-\log (x)\right ) \left (4-\left (1+e^2\right ) x+x \log (x)\right ) \left (x+\log \left (\frac {-4+x+e^2 x-x \log (x)}{1+e^2-\log (x)}\right )\right )^2} \, dx}{5-\log (3)}+\frac {3 \int \frac {x \log ^2(x)}{\left (1+e^2-\log (x)\right ) \left (4-\left (1+e^2\right ) x+x \log (x)\right ) \left (x+\log \left (\frac {-4+x+e^2 x-x \log (x)}{1+e^2-\log (x)}\right )\right )^2} \, dx}{5-\log (3)}+\frac {12 \int \frac {1}{x \left (-1-e^2+\log (x)\right ) \left (4-\left (1+e^2\right ) x+x \log (x)\right ) \left (x+\log \left (\frac {-4+x+e^2 x-x \log (x)}{1+e^2-\log (x)}\right )\right )^2} \, dx}{5-\log (3)}+\frac {\left (6 \left (1-e^2\right )\right ) \int \frac {\log (x)}{\left (1+e^2-\log (x)\right ) \left (4-\left (1+e^2\right ) x+x \log (x)\right ) \left (x+\log \left (\frac {-4+x+e^2 x-x \log (x)}{1+e^2-\log (x)}\right )\right )^2} \, dx}{5-\log (3)}+\frac {\left (6 \left (1+e^2\right )\right ) \int \frac {x \log (x)}{\left (-1-e^2+\log (x)\right ) \left (4-\left (1+e^2\right ) x+x \log (x)\right ) \left (x+\log \left (\frac {-4+x+e^2 x-x \log (x)}{1+e^2-\log (x)}\right )\right )^2} \, dx}{5-\log (3)}+\frac {\left (3 \left (1+e^2\right )^2\right ) \int \frac {x}{\left (1+e^2-\log (x)\right ) \left (4-\left (1+e^2\right ) x+x \log (x)\right ) \left (x+\log \left (\frac {-4+x+e^2 x-x \log (x)}{1+e^2-\log (x)}\right )\right )^2} \, dx}{5-\log (3)}+\frac {\left (3 \left (-3-2 e^2+e^4\right )\right ) \int \frac {1}{\left (1+e^2-\log (x)\right ) \left (4-\left (1+e^2\right ) x+x \log (x)\right ) \left (x+\log \left (\frac {-4+x+e^2 x-x \log (x)}{1+e^2-\log (x)}\right )\right )^2} \, dx}{5-\log (3)} \\ \end{align*}
Time = 0.15 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.27 \[ \int \frac {-12-9 x+3 x^2+e^4 \left (3 x+3 x^2\right )+e^2 \left (-6 x+6 x^2\right )+\left (6 x-6 x^2+e^2 \left (-6 x-6 x^2\right )\right ) \log (x)+\left (3 x+3 x^2\right ) \log ^2(x)}{20 x^3-5 x^4-5 e^4 x^4+e^2 \left (20 x^3-10 x^4\right )+\left (-4 x^3+x^4+e^4 x^4+e^2 \left (-4 x^3+2 x^4\right )\right ) \log (3)+\left (-20 x^3+10 x^4+10 e^2 x^4+\left (4 x^3-2 x^4-2 e^2 x^4\right ) \log (3)\right ) \log (x)+\left (-5 x^4+x^4 \log (3)\right ) \log ^2(x)+\left (40 x^2-10 x^3-10 e^4 x^3+e^2 \left (40 x^2-20 x^3\right )+\left (-8 x^2+2 x^3+2 e^4 x^3+e^2 \left (-8 x^2+4 x^3\right )\right ) \log (3)+\left (-40 x^2+20 x^3+20 e^2 x^3+\left (8 x^2-4 x^3-4 e^2 x^3\right ) \log (3)\right ) \log (x)+\left (-10 x^3+2 x^3 \log (3)\right ) \log ^2(x)\right ) \log \left (\frac {4-x-e^2 x+x \log (x)}{-1-e^2+\log (x)}\right )+\left (20 x-5 x^2-5 e^4 x^2+e^2 \left (20 x-10 x^2\right )+\left (-4 x+x^2+e^4 x^2+e^2 \left (-4 x+2 x^2\right )\right ) \log (3)+\left (-20 x+10 x^2+10 e^2 x^2+\left (4 x-2 x^2-2 e^2 x^2\right ) \log (3)\right ) \log (x)+\left (-5 x^2+x^2 \log (3)\right ) \log ^2(x)\right ) \log ^2\left (\frac {4-x-e^2 x+x \log (x)}{-1-e^2+\log (x)}\right )} \, dx=-\frac {3}{(-5+\log (3)) \left (x+\log \left (\frac {-4+x+e^2 x-x \log (x)}{1+e^2-\log (x)}\right )\right )} \]
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Time = 28.38 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.23
method | result | size |
parallelrisch | \(-\frac {3}{\left (x +\ln \left (\frac {{\mathrm e}^{2} x -x \ln \left (x \right )+x -4}{{\mathrm e}^{2}-\ln \left (x \right )+1}\right )\right ) \left (\ln \left (3\right )-5\right )}\) | \(37\) |
risch | \(-\frac {6 i}{\left (\ln \left (3\right )-5\right ) \left (\pi \,\operatorname {csgn}\left (i \left ({\mathrm e}^{2} x -4+x \left (1-\ln \left (x \right )\right )\right )\right ) \operatorname {csgn}\left (\frac {i}{{\mathrm e}^{2}-\ln \left (x \right )+1}\right ) \operatorname {csgn}\left (\frac {i \left ({\mathrm e}^{2} x -4+x \left (1-\ln \left (x \right )\right )\right )}{{\mathrm e}^{2}-\ln \left (x \right )+1}\right )-\pi \,\operatorname {csgn}\left (i \left ({\mathrm e}^{2} x -4+x \left (1-\ln \left (x \right )\right )\right )\right ) {\operatorname {csgn}\left (\frac {i \left ({\mathrm e}^{2} x -4+x \left (1-\ln \left (x \right )\right )\right )}{{\mathrm e}^{2}-\ln \left (x \right )+1}\right )}^{2}-\pi \,\operatorname {csgn}\left (\frac {i}{{\mathrm e}^{2}-\ln \left (x \right )+1}\right ) {\operatorname {csgn}\left (\frac {i \left ({\mathrm e}^{2} x -4+x \left (1-\ln \left (x \right )\right )\right )}{{\mathrm e}^{2}-\ln \left (x \right )+1}\right )}^{2}+\pi {\operatorname {csgn}\left (\frac {i \left ({\mathrm e}^{2} x -4+x \left (1-\ln \left (x \right )\right )\right )}{{\mathrm e}^{2}-\ln \left (x \right )+1}\right )}^{3}+2 i x -2 i \ln \left ({\mathrm e}^{2}-\ln \left (x \right )+1\right )+2 i \ln \left ({\mathrm e}^{2} x -4+x \left (1-\ln \left (x \right )\right )\right )\right )}\) | \(239\) |
default | \(-\frac {6 i}{\left (\ln \left (3\right )-5\right ) \left (\pi \,\operatorname {csgn}\left (\frac {i}{{\mathrm e}^{2}-\ln \left (x \right )+1}\right ) \operatorname {csgn}\left (i \left (x \ln \left (x \right )-x -{\mathrm e}^{\ln \left (x \right )+2}+4\right )\right ) \operatorname {csgn}\left (\frac {i \left (x \ln \left (x \right )-x -{\mathrm e}^{\ln \left (x \right )+2}+4\right )}{{\mathrm e}^{2}-\ln \left (x \right )+1}\right )-\pi \,\operatorname {csgn}\left (\frac {i}{{\mathrm e}^{2}-\ln \left (x \right )+1}\right ) {\operatorname {csgn}\left (\frac {i \left (x \ln \left (x \right )-x -{\mathrm e}^{\ln \left (x \right )+2}+4\right )}{{\mathrm e}^{2}-\ln \left (x \right )+1}\right )}^{2}+\pi \,\operatorname {csgn}\left (i \left (x \ln \left (x \right )-x -{\mathrm e}^{\ln \left (x \right )+2}+4\right )\right ) {\operatorname {csgn}\left (\frac {i \left (x \ln \left (x \right )-x -{\mathrm e}^{\ln \left (x \right )+2}+4\right )}{{\mathrm e}^{2}-\ln \left (x \right )+1}\right )}^{2}-\pi {\operatorname {csgn}\left (\frac {i \left (x \ln \left (x \right )-x -{\mathrm e}^{\ln \left (x \right )+2}+4\right )}{{\mathrm e}^{2}-\ln \left (x \right )+1}\right )}^{3}+2 i x -2 i \ln \left ({\mathrm e}^{2}-\ln \left (x \right )+1\right )+2 i \ln \left (-x \ln \left (x \right )+x +{\mathrm e}^{\ln \left (x \right )+2}-4\right )\right )}\) | \(250\) |
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Time = 0.28 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.37 \[ \int \frac {-12-9 x+3 x^2+e^4 \left (3 x+3 x^2\right )+e^2 \left (-6 x+6 x^2\right )+\left (6 x-6 x^2+e^2 \left (-6 x-6 x^2\right )\right ) \log (x)+\left (3 x+3 x^2\right ) \log ^2(x)}{20 x^3-5 x^4-5 e^4 x^4+e^2 \left (20 x^3-10 x^4\right )+\left (-4 x^3+x^4+e^4 x^4+e^2 \left (-4 x^3+2 x^4\right )\right ) \log (3)+\left (-20 x^3+10 x^4+10 e^2 x^4+\left (4 x^3-2 x^4-2 e^2 x^4\right ) \log (3)\right ) \log (x)+\left (-5 x^4+x^4 \log (3)\right ) \log ^2(x)+\left (40 x^2-10 x^3-10 e^4 x^3+e^2 \left (40 x^2-20 x^3\right )+\left (-8 x^2+2 x^3+2 e^4 x^3+e^2 \left (-8 x^2+4 x^3\right )\right ) \log (3)+\left (-40 x^2+20 x^3+20 e^2 x^3+\left (8 x^2-4 x^3-4 e^2 x^3\right ) \log (3)\right ) \log (x)+\left (-10 x^3+2 x^3 \log (3)\right ) \log ^2(x)\right ) \log \left (\frac {4-x-e^2 x+x \log (x)}{-1-e^2+\log (x)}\right )+\left (20 x-5 x^2-5 e^4 x^2+e^2 \left (20 x-10 x^2\right )+\left (-4 x+x^2+e^4 x^2+e^2 \left (-4 x+2 x^2\right )\right ) \log (3)+\left (-20 x+10 x^2+10 e^2 x^2+\left (4 x-2 x^2-2 e^2 x^2\right ) \log (3)\right ) \log (x)+\left (-5 x^2+x^2 \log (3)\right ) \log ^2(x)\right ) \log ^2\left (\frac {4-x-e^2 x+x \log (x)}{-1-e^2+\log (x)}\right )} \, dx=-\frac {3}{x \log \left (3\right ) + {\left (\log \left (3\right ) - 5\right )} \log \left (\frac {x e^{2} - x \log \left (x\right ) + x - 4}{e^{2} - \log \left (x\right ) + 1}\right ) - 5 \, x} \]
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Time = 0.48 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.30 \[ \int \frac {-12-9 x+3 x^2+e^4 \left (3 x+3 x^2\right )+e^2 \left (-6 x+6 x^2\right )+\left (6 x-6 x^2+e^2 \left (-6 x-6 x^2\right )\right ) \log (x)+\left (3 x+3 x^2\right ) \log ^2(x)}{20 x^3-5 x^4-5 e^4 x^4+e^2 \left (20 x^3-10 x^4\right )+\left (-4 x^3+x^4+e^4 x^4+e^2 \left (-4 x^3+2 x^4\right )\right ) \log (3)+\left (-20 x^3+10 x^4+10 e^2 x^4+\left (4 x^3-2 x^4-2 e^2 x^4\right ) \log (3)\right ) \log (x)+\left (-5 x^4+x^4 \log (3)\right ) \log ^2(x)+\left (40 x^2-10 x^3-10 e^4 x^3+e^2 \left (40 x^2-20 x^3\right )+\left (-8 x^2+2 x^3+2 e^4 x^3+e^2 \left (-8 x^2+4 x^3\right )\right ) \log (3)+\left (-40 x^2+20 x^3+20 e^2 x^3+\left (8 x^2-4 x^3-4 e^2 x^3\right ) \log (3)\right ) \log (x)+\left (-10 x^3+2 x^3 \log (3)\right ) \log ^2(x)\right ) \log \left (\frac {4-x-e^2 x+x \log (x)}{-1-e^2+\log (x)}\right )+\left (20 x-5 x^2-5 e^4 x^2+e^2 \left (20 x-10 x^2\right )+\left (-4 x+x^2+e^4 x^2+e^2 \left (-4 x+2 x^2\right )\right ) \log (3)+\left (-20 x+10 x^2+10 e^2 x^2+\left (4 x-2 x^2-2 e^2 x^2\right ) \log (3)\right ) \log (x)+\left (-5 x^2+x^2 \log (3)\right ) \log ^2(x)\right ) \log ^2\left (\frac {4-x-e^2 x+x \log (x)}{-1-e^2+\log (x)}\right )} \, dx=- \frac {3}{- 5 x + x \log {\left (3 \right )} + \left (-5 + \log {\left (3 \right )}\right ) \log {\left (\frac {x \log {\left (x \right )} - x e^{2} - x + 4}{\log {\left (x \right )} - e^{2} - 1} \right )}} \]
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Time = 0.55 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.50 \[ \int \frac {-12-9 x+3 x^2+e^4 \left (3 x+3 x^2\right )+e^2 \left (-6 x+6 x^2\right )+\left (6 x-6 x^2+e^2 \left (-6 x-6 x^2\right )\right ) \log (x)+\left (3 x+3 x^2\right ) \log ^2(x)}{20 x^3-5 x^4-5 e^4 x^4+e^2 \left (20 x^3-10 x^4\right )+\left (-4 x^3+x^4+e^4 x^4+e^2 \left (-4 x^3+2 x^4\right )\right ) \log (3)+\left (-20 x^3+10 x^4+10 e^2 x^4+\left (4 x^3-2 x^4-2 e^2 x^4\right ) \log (3)\right ) \log (x)+\left (-5 x^4+x^4 \log (3)\right ) \log ^2(x)+\left (40 x^2-10 x^3-10 e^4 x^3+e^2 \left (40 x^2-20 x^3\right )+\left (-8 x^2+2 x^3+2 e^4 x^3+e^2 \left (-8 x^2+4 x^3\right )\right ) \log (3)+\left (-40 x^2+20 x^3+20 e^2 x^3+\left (8 x^2-4 x^3-4 e^2 x^3\right ) \log (3)\right ) \log (x)+\left (-10 x^3+2 x^3 \log (3)\right ) \log ^2(x)\right ) \log \left (\frac {4-x-e^2 x+x \log (x)}{-1-e^2+\log (x)}\right )+\left (20 x-5 x^2-5 e^4 x^2+e^2 \left (20 x-10 x^2\right )+\left (-4 x+x^2+e^4 x^2+e^2 \left (-4 x+2 x^2\right )\right ) \log (3)+\left (-20 x+10 x^2+10 e^2 x^2+\left (4 x-2 x^2-2 e^2 x^2\right ) \log (3)\right ) \log (x)+\left (-5 x^2+x^2 \log (3)\right ) \log ^2(x)\right ) \log ^2\left (\frac {4-x-e^2 x+x \log (x)}{-1-e^2+\log (x)}\right )} \, dx=-\frac {3}{x {\left (\log \left (3\right ) - 5\right )} + {\left (\log \left (3\right ) - 5\right )} \log \left (-x {\left (e^{2} + 1\right )} + x \log \left (x\right ) + 4\right ) - {\left (\log \left (3\right ) - 5\right )} \log \left (-e^{2} + \log \left (x\right ) - 1\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 67 vs. \(2 (27) = 54\).
Time = 2.20 (sec) , antiderivative size = 67, normalized size of antiderivative = 2.23 \[ \int \frac {-12-9 x+3 x^2+e^4 \left (3 x+3 x^2\right )+e^2 \left (-6 x+6 x^2\right )+\left (6 x-6 x^2+e^2 \left (-6 x-6 x^2\right )\right ) \log (x)+\left (3 x+3 x^2\right ) \log ^2(x)}{20 x^3-5 x^4-5 e^4 x^4+e^2 \left (20 x^3-10 x^4\right )+\left (-4 x^3+x^4+e^4 x^4+e^2 \left (-4 x^3+2 x^4\right )\right ) \log (3)+\left (-20 x^3+10 x^4+10 e^2 x^4+\left (4 x^3-2 x^4-2 e^2 x^4\right ) \log (3)\right ) \log (x)+\left (-5 x^4+x^4 \log (3)\right ) \log ^2(x)+\left (40 x^2-10 x^3-10 e^4 x^3+e^2 \left (40 x^2-20 x^3\right )+\left (-8 x^2+2 x^3+2 e^4 x^3+e^2 \left (-8 x^2+4 x^3\right )\right ) \log (3)+\left (-40 x^2+20 x^3+20 e^2 x^3+\left (8 x^2-4 x^3-4 e^2 x^3\right ) \log (3)\right ) \log (x)+\left (-10 x^3+2 x^3 \log (3)\right ) \log ^2(x)\right ) \log \left (\frac {4-x-e^2 x+x \log (x)}{-1-e^2+\log (x)}\right )+\left (20 x-5 x^2-5 e^4 x^2+e^2 \left (20 x-10 x^2\right )+\left (-4 x+x^2+e^4 x^2+e^2 \left (-4 x+2 x^2\right )\right ) \log (3)+\left (-20 x+10 x^2+10 e^2 x^2+\left (4 x-2 x^2-2 e^2 x^2\right ) \log (3)\right ) \log (x)+\left (-5 x^2+x^2 \log (3)\right ) \log ^2(x)\right ) \log ^2\left (\frac {4-x-e^2 x+x \log (x)}{-1-e^2+\log (x)}\right )} \, dx=-\frac {3}{x \log \left (3\right ) + \log \left (3\right ) \log \left (x e^{2} - x \log \left (x\right ) + x - 4\right ) - \log \left (3\right ) \log \left (e^{2} - \log \left (x\right ) + 1\right ) - 5 \, x - 5 \, \log \left (x e^{2} - x \log \left (x\right ) + x - 4\right ) + 5 \, \log \left (e^{2} - \log \left (x\right ) + 1\right )} \]
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Time = 14.94 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.20 \[ \int \frac {-12-9 x+3 x^2+e^4 \left (3 x+3 x^2\right )+e^2 \left (-6 x+6 x^2\right )+\left (6 x-6 x^2+e^2 \left (-6 x-6 x^2\right )\right ) \log (x)+\left (3 x+3 x^2\right ) \log ^2(x)}{20 x^3-5 x^4-5 e^4 x^4+e^2 \left (20 x^3-10 x^4\right )+\left (-4 x^3+x^4+e^4 x^4+e^2 \left (-4 x^3+2 x^4\right )\right ) \log (3)+\left (-20 x^3+10 x^4+10 e^2 x^4+\left (4 x^3-2 x^4-2 e^2 x^4\right ) \log (3)\right ) \log (x)+\left (-5 x^4+x^4 \log (3)\right ) \log ^2(x)+\left (40 x^2-10 x^3-10 e^4 x^3+e^2 \left (40 x^2-20 x^3\right )+\left (-8 x^2+2 x^3+2 e^4 x^3+e^2 \left (-8 x^2+4 x^3\right )\right ) \log (3)+\left (-40 x^2+20 x^3+20 e^2 x^3+\left (8 x^2-4 x^3-4 e^2 x^3\right ) \log (3)\right ) \log (x)+\left (-10 x^3+2 x^3 \log (3)\right ) \log ^2(x)\right ) \log \left (\frac {4-x-e^2 x+x \log (x)}{-1-e^2+\log (x)}\right )+\left (20 x-5 x^2-5 e^4 x^2+e^2 \left (20 x-10 x^2\right )+\left (-4 x+x^2+e^4 x^2+e^2 \left (-4 x+2 x^2\right )\right ) \log (3)+\left (-20 x+10 x^2+10 e^2 x^2+\left (4 x-2 x^2-2 e^2 x^2\right ) \log (3)\right ) \log (x)+\left (-5 x^2+x^2 \log (3)\right ) \log ^2(x)\right ) \log ^2\left (\frac {4-x-e^2 x+x \log (x)}{-1-e^2+\log (x)}\right )} \, dx=-\frac {3}{\left (\ln \left (3\right )-5\right )\,\left (x+\ln \left (\frac {x+x\,{\mathrm {e}}^2-x\,\ln \left (x\right )-4}{{\mathrm {e}}^2-\ln \left (x\right )+1}\right )\right )} \]
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