Integrand size = 282, antiderivative size = 27 \[ \int \frac {-6 x+2 x^3+e^{10} \left (-6 x+2 x^3\right )+e^5 \left (-12 x+4 x^3\right )+e^{2-2 x} \left (-6 x+6 x^2+2 x^3-2 x^4\right )+e^{1-x} \left (-12 x+6 x^2+4 x^3-2 x^4+e^5 \left (-12 x+6 x^2+4 x^3-2 x^4\right )\right )+\left (2 x+2 x^3+4 e^5 x^3+2 e^{10} x^3+2 e^{2-2 x} x^3+e^{1-x} \left (4 x^3+4 e^5 x^3\right )\right ) \log \left (1+x^2+2 e^5 x^2+e^{10} x^2+e^{2-2 x} x^2+e^{1-x} \left (2 x^2+2 e^5 x^2\right )\right )}{1+x^2+2 e^5 x^2+e^{10} x^2+e^{2-2 x} x^2+e^{1-x} \left (2 x^2+2 e^5 x^2\right )} \, dx=\left (-3+x^2\right ) \log \left (1+\left (1+e^5+e^{1-x}\right )^2 x^2\right ) \]
[Out]
\[ \int \frac {-6 x+2 x^3+e^{10} \left (-6 x+2 x^3\right )+e^5 \left (-12 x+4 x^3\right )+e^{2-2 x} \left (-6 x+6 x^2+2 x^3-2 x^4\right )+e^{1-x} \left (-12 x+6 x^2+4 x^3-2 x^4+e^5 \left (-12 x+6 x^2+4 x^3-2 x^4\right )\right )+\left (2 x+2 x^3+4 e^5 x^3+2 e^{10} x^3+2 e^{2-2 x} x^3+e^{1-x} \left (4 x^3+4 e^5 x^3\right )\right ) \log \left (1+x^2+2 e^5 x^2+e^{10} x^2+e^{2-2 x} x^2+e^{1-x} \left (2 x^2+2 e^5 x^2\right )\right )}{1+x^2+2 e^5 x^2+e^{10} x^2+e^{2-2 x} x^2+e^{1-x} \left (2 x^2+2 e^5 x^2\right )} \, dx=\int \frac {-6 x+2 x^3+e^{10} \left (-6 x+2 x^3\right )+e^5 \left (-12 x+4 x^3\right )+e^{2-2 x} \left (-6 x+6 x^2+2 x^3-2 x^4\right )+e^{1-x} \left (-12 x+6 x^2+4 x^3-2 x^4+e^5 \left (-12 x+6 x^2+4 x^3-2 x^4\right )\right )+\left (2 x+2 x^3+4 e^5 x^3+2 e^{10} x^3+2 e^{2-2 x} x^3+e^{1-x} \left (4 x^3+4 e^5 x^3\right )\right ) \log \left (1+x^2+2 e^5 x^2+e^{10} x^2+e^{2-2 x} x^2+e^{1-x} \left (2 x^2+2 e^5 x^2\right )\right )}{1+x^2+2 e^5 x^2+e^{10} x^2+e^{2-2 x} x^2+e^{1-x} \left (2 x^2+2 e^5 x^2\right )} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {-6 x+2 x^3+e^{10} \left (-6 x+2 x^3\right )+e^5 \left (-12 x+4 x^3\right )+e^{2-2 x} \left (-6 x+6 x^2+2 x^3-2 x^4\right )+e^{1-x} \left (-12 x+6 x^2+4 x^3-2 x^4+e^5 \left (-12 x+6 x^2+4 x^3-2 x^4\right )\right )+\left (2 x+2 x^3+4 e^5 x^3+2 e^{10} x^3+2 e^{2-2 x} x^3+e^{1-x} \left (4 x^3+4 e^5 x^3\right )\right ) \log \left (1+x^2+2 e^5 x^2+e^{10} x^2+e^{2-2 x} x^2+e^{1-x} \left (2 x^2+2 e^5 x^2\right )\right )}{1+e^{10} x^2+e^{2-2 x} x^2+\left (1+2 e^5\right ) x^2+e^{1-x} \left (2 x^2+2 e^5 x^2\right )} \, dx \\ & = \int \frac {-6 x+2 x^3+e^{10} \left (-6 x+2 x^3\right )+e^5 \left (-12 x+4 x^3\right )+e^{2-2 x} \left (-6 x+6 x^2+2 x^3-2 x^4\right )+e^{1-x} \left (-12 x+6 x^2+4 x^3-2 x^4+e^5 \left (-12 x+6 x^2+4 x^3-2 x^4\right )\right )+\left (2 x+2 x^3+4 e^5 x^3+2 e^{10} x^3+2 e^{2-2 x} x^3+e^{1-x} \left (4 x^3+4 e^5 x^3\right )\right ) \log \left (1+x^2+2 e^5 x^2+e^{10} x^2+e^{2-2 x} x^2+e^{1-x} \left (2 x^2+2 e^5 x^2\right )\right )}{1+e^{2-2 x} x^2+\left (1+2 e^5+e^{10}\right ) x^2+e^{1-x} \left (2 x^2+2 e^5 x^2\right )} \, dx \\ & = \int \frac {2 x \left (-3+x^2+2 e^5 \left (1+\frac {e^5}{2}\right ) \left (-3+x^2\right )+e^{2-2 x} \left (-3+3 x+x^2-x^3\right )-e^{1-x} \left (1+e^5\right ) \left (6-3 x-2 x^2+x^3\right )+e^{-2 x} \left (e^2 x^2+2 e^{1+x} x^2+e^{2 (5+x)} x^2+2 e^{6+x} x^2+2 e^{5+2 x} x^2+e^{2 x} \left (1+x^2\right )\right ) \log \left (1+e^{-2 x} \left (e+e^x+e^{5+x}\right )^2 x^2\right )\right )}{1+e^{-2 x} \left (e+e^x+e^{5+x}\right )^2 x^2} \, dx \\ & = 2 \int \frac {x \left (-3+x^2+2 e^5 \left (1+\frac {e^5}{2}\right ) \left (-3+x^2\right )+e^{2-2 x} \left (-3+3 x+x^2-x^3\right )-e^{1-x} \left (1+e^5\right ) \left (6-3 x-2 x^2+x^3\right )+e^{-2 x} \left (e^2 x^2+2 e^{1+x} x^2+e^{2 (5+x)} x^2+2 e^{6+x} x^2+2 e^{5+2 x} x^2+e^{2 x} \left (1+x^2\right )\right ) \log \left (1+e^{-2 x} \left (e+e^x+e^{5+x}\right )^2 x^2\right )\right )}{1+e^{-2 x} \left (e+e^x+e^{5+x}\right )^2 x^2} \, dx \\ & = 2 \int \left (\frac {e x \left (3-x^2\right ) \left (-e-2 e^x \left (1+e^5\right )+e x+e^x \left (1+e^5\right ) x+e \left (1+e^5 \left (2+e^5\right )\right ) x^3+e^x \left (1+e^5 \left (3+3 e^5+e^{10}\right )\right ) x^3\right )}{\left (1+\left (1+e^5\right )^2 x^2\right ) \left (e^{2 x}+e^2 x^2+2 e^{1+x} \left (1+e^5\right ) x^2+e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2\right )}+\frac {x \left (-3 \left (1+e^5 \left (2+e^5\right )\right )+\left (1+e^5 \left (2+e^5\right )\right ) x^2+\log \left (1+e^{-2 x} \left (e+e^x+e^{5+x}\right )^2 x^2\right )+\left (1+e^5 \left (2+e^5\right )\right ) x^2 \log \left (1+e^{-2 x} \left (e+e^x+e^{5+x}\right )^2 x^2\right )\right )}{1+\left (1+e^5\right )^2 x^2}\right ) \, dx \\ & = 2 \int \frac {x \left (-3 \left (1+e^5 \left (2+e^5\right )\right )+\left (1+e^5 \left (2+e^5\right )\right ) x^2+\log \left (1+e^{-2 x} \left (e+e^x+e^{5+x}\right )^2 x^2\right )+\left (1+e^5 \left (2+e^5\right )\right ) x^2 \log \left (1+e^{-2 x} \left (e+e^x+e^{5+x}\right )^2 x^2\right )\right )}{1+\left (1+e^5\right )^2 x^2} \, dx+(2 e) \int \frac {x \left (3-x^2\right ) \left (-e-2 e^x \left (1+e^5\right )+e x+e^x \left (1+e^5\right ) x+e \left (1+e^5 \left (2+e^5\right )\right ) x^3+e^x \left (1+e^5 \left (3+3 e^5+e^{10}\right )\right ) x^3\right )}{\left (1+\left (1+e^5\right )^2 x^2\right ) \left (e^{2 x}+e^2 x^2+2 e^{1+x} \left (1+e^5\right ) x^2+e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2\right )} \, dx \\ & = 2 \int x \left (\frac {\left (1+e^5\right )^2 \left (-3+x^2\right )}{1+\left (1+e^5\right )^2 x^2}+\log \left (1+e^{-2 x} \left (e+e^x+e^{5+x}\right )^2 x^2\right )\right ) \, dx+(2 e) \int \left (\frac {x \left (e+2 e^x \left (1+e^5\right )-e x-e^x \left (1+e^5\right ) x-e \left (1+e^5 \left (2+e^5\right )\right ) x^3-e^x \left (1+e^5 \left (3+3 e^5+e^{10}\right )\right ) x^3\right )}{\left (1+e^5\right )^2 \left (e^{2 x}+e^2 x^2+2 e^{1+x} \left (1+e^5\right ) x^2+e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2\right )}+\frac {\left (4+6 e^5+3 e^{10}\right ) x \left (-e-2 e^x \left (1+e^5\right )+e x+e^x \left (1+e^5\right ) x+e \left (1+e^5 \left (2+e^5\right )\right ) x^3+e^x \left (1+e^5 \left (3+3 e^5+e^{10}\right )\right ) x^3\right )}{\left (1+e^5\right )^2 \left (1+\left (1+e^5\right )^2 x^2\right ) \left (e^{2 x}+e^2 x^2+2 e^{1+x} \left (1+e^5\right ) x^2+e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2\right )}\right ) \, dx \\ & = 2 \int \left (\frac {\left (1+e^5\right )^2 x \left (-3+x^2\right )}{1+\left (1+e^5\right )^2 x^2}+x \log \left (1+e^{-2 x} \left (e+e^x+e^{5+x}\right )^2 x^2\right )\right ) \, dx+\frac {(2 e) \int \frac {x \left (e+2 e^x \left (1+e^5\right )-e x-e^x \left (1+e^5\right ) x-e \left (1+e^5 \left (2+e^5\right )\right ) x^3-e^x \left (1+e^5 \left (3+3 e^5+e^{10}\right )\right ) x^3\right )}{e^{2 x}+e^2 x^2+2 e^{1+x} \left (1+e^5\right ) x^2+e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2} \, dx}{\left (1+e^5\right )^2}+\frac {\left (2 e \left (4+6 e^5+3 e^{10}\right )\right ) \int \frac {x \left (-e-2 e^x \left (1+e^5\right )+e x+e^x \left (1+e^5\right ) x+e \left (1+e^5 \left (2+e^5\right )\right ) x^3+e^x \left (1+e^5 \left (3+3 e^5+e^{10}\right )\right ) x^3\right )}{\left (1+\left (1+e^5\right )^2 x^2\right ) \left (e^{2 x}+e^2 x^2+2 e^{1+x} \left (1+e^5\right ) x^2+e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2\right )} \, dx}{\left (1+e^5\right )^2} \\ & = 2 \int x \log \left (1+e^{-2 x} \left (e+e^x+e^{5+x}\right )^2 x^2\right ) \, dx+\frac {(2 e) \int \left (\frac {e x^2}{-e^{2 x}-e^2 x^2-2 e^{1+x} \left (1+e^5\right ) x^2-e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2}+\frac {e \left (1+e^5\right )^2 x^4}{-e^{2 x}-e^2 x^2-2 e^{1+x} \left (1+e^5\right ) x^2-e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2}+\frac {e x}{e^{2 x}+e^2 x^2+2 e^{1+x} \left (1+e^5\right ) x^2+e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2}+\frac {2 e^x \left (1+e^5\right ) x}{e^{2 x}+e^2 x^2+2 e^{1+x} \left (1+e^5\right ) x^2+e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2}+\frac {e^x \left (-1-e^5\right ) x^2}{e^{2 x}+e^2 x^2+2 e^{1+x} \left (1+e^5\right ) x^2+e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2}+\frac {e^x \left (-1-e^5\right )^3 x^4}{e^{2 x}+e^2 x^2+2 e^{1+x} \left (1+e^5\right ) x^2+e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2}\right ) \, dx}{\left (1+e^5\right )^2}+\left (2 \left (1+e^5\right )^2\right ) \int \frac {x \left (-3+x^2\right )}{1+\left (1+e^5\right )^2 x^2} \, dx+\frac {\left (2 e \left (4+6 e^5+3 e^{10}\right )\right ) \int \left (\frac {e x}{\left (-1-\left (1+e^5\right )^2 x^2\right ) \left (e^{2 x}+e^2 x^2+2 e^{1+x} \left (1+e^5\right ) x^2+e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2\right )}+\frac {2 e^x \left (-1-e^5\right ) x}{\left (1+\left (1+e^5\right )^2 x^2\right ) \left (e^{2 x}+e^2 x^2+2 e^{1+x} \left (1+e^5\right ) x^2+e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2\right )}+\frac {e x^2}{\left (1+\left (1+e^5\right )^2 x^2\right ) \left (e^{2 x}+e^2 x^2+2 e^{1+x} \left (1+e^5\right ) x^2+e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2\right )}+\frac {e^x \left (1+e^5\right ) x^2}{\left (1+\left (1+e^5\right )^2 x^2\right ) \left (e^{2 x}+e^2 x^2+2 e^{1+x} \left (1+e^5\right ) x^2+e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2\right )}+\frac {e \left (1+e^5\right )^2 x^4}{\left (1+\left (1+e^5\right )^2 x^2\right ) \left (e^{2 x}+e^2 x^2+2 e^{1+x} \left (1+e^5\right ) x^2+e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2\right )}+\frac {e^x \left (1+e^5\right )^3 x^4}{\left (1+\left (1+e^5\right )^2 x^2\right ) \left (e^{2 x}+e^2 x^2+2 e^{1+x} \left (1+e^5\right ) x^2+e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2\right )}\right ) \, dx}{\left (1+e^5\right )^2} \\ & = x^2 \log \left (1+e^{-2 x} \left (e+e^x+e^{5+x}\right )^2 x^2\right )+\left (2 e^2\right ) \int \frac {x^4}{-e^{2 x}-e^2 x^2-2 e^{1+x} \left (1+e^5\right ) x^2-e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2} \, dx+\frac {\left (2 e^2\right ) \int \frac {x^2}{-e^{2 x}-e^2 x^2-2 e^{1+x} \left (1+e^5\right ) x^2-e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2} \, dx}{\left (1+e^5\right )^2}+\frac {\left (2 e^2\right ) \int \frac {x}{e^{2 x}+e^2 x^2+2 e^{1+x} \left (1+e^5\right ) x^2+e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2} \, dx}{\left (1+e^5\right )^2}-\frac {(2 e) \int \frac {e^x x^2}{e^{2 x}+e^2 x^2+2 e^{1+x} \left (1+e^5\right ) x^2+e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2} \, dx}{1+e^5}+\frac {(4 e) \int \frac {e^x x}{e^{2 x}+e^2 x^2+2 e^{1+x} \left (1+e^5\right ) x^2+e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2} \, dx}{1+e^5}-\left (2 e \left (1+e^5\right )\right ) \int \frac {e^x x^4}{e^{2 x}+e^2 x^2+2 e^{1+x} \left (1+e^5\right ) x^2+e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2} \, dx+\left (1+e^5\right )^2 \text {Subst}\left (\int \frac {-3+x}{1+\left (1+e^5\right )^2 x} \, dx,x,x^2\right )+\left (2 e^2 \left (4+6 e^5+3 e^{10}\right )\right ) \int \frac {x^4}{\left (1+\left (1+e^5\right )^2 x^2\right ) \left (e^{2 x}+e^2 x^2+2 e^{1+x} \left (1+e^5\right ) x^2+e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2\right )} \, dx+\frac {\left (2 e^2 \left (4+6 e^5+3 e^{10}\right )\right ) \int \frac {x}{\left (-1-\left (1+e^5\right )^2 x^2\right ) \left (e^{2 x}+e^2 x^2+2 e^{1+x} \left (1+e^5\right ) x^2+e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2\right )} \, dx}{\left (1+e^5\right )^2}+\frac {\left (2 e^2 \left (4+6 e^5+3 e^{10}\right )\right ) \int \frac {x^2}{\left (1+\left (1+e^5\right )^2 x^2\right ) \left (e^{2 x}+e^2 x^2+2 e^{1+x} \left (1+e^5\right ) x^2+e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2\right )} \, dx}{\left (1+e^5\right )^2}+\frac {\left (2 e \left (4+6 e^5+3 e^{10}\right )\right ) \int \frac {e^x x^2}{\left (1+\left (1+e^5\right )^2 x^2\right ) \left (e^{2 x}+e^2 x^2+2 e^{1+x} \left (1+e^5\right ) x^2+e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2\right )} \, dx}{1+e^5}-\frac {\left (4 e \left (4+6 e^5+3 e^{10}\right )\right ) \int \frac {e^x x}{\left (1+\left (1+e^5\right )^2 x^2\right ) \left (e^{2 x}+e^2 x^2+2 e^{1+x} \left (1+e^5\right ) x^2+e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2\right )} \, dx}{1+e^5}+\left (2 e \left (1+e^5\right ) \left (4+6 e^5+3 e^{10}\right )\right ) \int \frac {e^x x^4}{\left (1+\left (1+e^5\right )^2 x^2\right ) \left (e^{2 x}+e^2 x^2+2 e^{1+x} \left (1+e^5\right ) x^2+e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2\right )} \, dx-\int \frac {2 \left (e+e^x \left (1+e^5\right )\right ) x^3 \left (e+e^x \left (1+e^5\right )-e x\right )}{e^2 x^2+\left (1+\frac {2}{e^5}\right ) e^{2 (5+x)} x^2+2 e^{1+x} \left (1+e^5\right ) x^2+e^{2 x} \left (1+x^2\right )} \, dx \\ & = \text {Too large to display} \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(94\) vs. \(2(27)=54\).
Time = 0.25 (sec) , antiderivative size = 94, normalized size of antiderivative = 3.48 \[ \int \frac {-6 x+2 x^3+e^{10} \left (-6 x+2 x^3\right )+e^5 \left (-12 x+4 x^3\right )+e^{2-2 x} \left (-6 x+6 x^2+2 x^3-2 x^4\right )+e^{1-x} \left (-12 x+6 x^2+4 x^3-2 x^4+e^5 \left (-12 x+6 x^2+4 x^3-2 x^4\right )\right )+\left (2 x+2 x^3+4 e^5 x^3+2 e^{10} x^3+2 e^{2-2 x} x^3+e^{1-x} \left (4 x^3+4 e^5 x^3\right )\right ) \log \left (1+x^2+2 e^5 x^2+e^{10} x^2+e^{2-2 x} x^2+e^{1-x} \left (2 x^2+2 e^5 x^2\right )\right )}{1+x^2+2 e^5 x^2+e^{10} x^2+e^{2-2 x} x^2+e^{1-x} \left (2 x^2+2 e^5 x^2\right )} \, dx=2 \left (-\frac {3}{2} \log \left (1+x^2+2 e^5 x^2+e^{10} x^2+e^{2-2 x} x^2+2 e^{1-x} x^2+2 e^{6-x} x^2\right )+\frac {1}{2} x^2 \log \left (1+e^{-2 x} \left (e+e^x+e^{5+x}\right )^2 x^2\right )\right ) \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. \(106\) vs. \(2(25)=50\).
Time = 3.19 (sec) , antiderivative size = 107, normalized size of antiderivative = 3.96
method | result | size |
risch | \(x^{2} \ln \left (2 x^{2} {\mathrm e}^{-x +6}+2 x^{2} {\mathrm e}^{5}+x^{2} {\mathrm e}^{2-2 x}+x^{2} {\mathrm e}^{10}+2 x^{2} {\mathrm e}^{1-x}+x^{2}+1\right )-6 \ln \left (x \right )+6-3 \ln \left ({\mathrm e}^{2-2 x}+\left (2 \,{\mathrm e}^{5}+2\right ) {\mathrm e}^{1-x}+\frac {2 x^{2} {\mathrm e}^{5}+x^{2} {\mathrm e}^{10}+x^{2}+1}{x^{2}}\right )\) | \(107\) |
parallelrisch | \(x^{2} \ln \left (x^{2} {\mathrm e}^{2-2 x}+\left (2 x^{2} {\mathrm e}^{5}+2 x^{2}\right ) {\mathrm e}^{1-x}+x^{2} {\mathrm e}^{10}+2 x^{2} {\mathrm e}^{5}+x^{2}+1\right )-3 \ln \left (x^{2} {\mathrm e}^{2-2 x}+\left (2 x^{2} {\mathrm e}^{5}+2 x^{2}\right ) {\mathrm e}^{1-x}+x^{2} {\mathrm e}^{10}+2 x^{2} {\mathrm e}^{5}+x^{2}+1\right )\) | \(114\) |
[In]
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Leaf count of result is larger than twice the leaf count of optimal. 53 vs. \(2 (25) = 50\).
Time = 0.40 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.96 \[ \int \frac {-6 x+2 x^3+e^{10} \left (-6 x+2 x^3\right )+e^5 \left (-12 x+4 x^3\right )+e^{2-2 x} \left (-6 x+6 x^2+2 x^3-2 x^4\right )+e^{1-x} \left (-12 x+6 x^2+4 x^3-2 x^4+e^5 \left (-12 x+6 x^2+4 x^3-2 x^4\right )\right )+\left (2 x+2 x^3+4 e^5 x^3+2 e^{10} x^3+2 e^{2-2 x} x^3+e^{1-x} \left (4 x^3+4 e^5 x^3\right )\right ) \log \left (1+x^2+2 e^5 x^2+e^{10} x^2+e^{2-2 x} x^2+e^{1-x} \left (2 x^2+2 e^5 x^2\right )\right )}{1+x^2+2 e^5 x^2+e^{10} x^2+e^{2-2 x} x^2+e^{1-x} \left (2 x^2+2 e^5 x^2\right )} \, dx={\left (x^{2} - 3\right )} \log \left (x^{2} e^{10} + 2 \, x^{2} e^{5} + x^{2} e^{\left (-2 \, x + 2\right )} + x^{2} + 2 \, {\left (x^{2} e^{5} + x^{2}\right )} e^{\left (-x + 1\right )} + 1\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 104 vs. \(2 (22) = 44\).
Time = 0.39 (sec) , antiderivative size = 104, normalized size of antiderivative = 3.85 \[ \int \frac {-6 x+2 x^3+e^{10} \left (-6 x+2 x^3\right )+e^5 \left (-12 x+4 x^3\right )+e^{2-2 x} \left (-6 x+6 x^2+2 x^3-2 x^4\right )+e^{1-x} \left (-12 x+6 x^2+4 x^3-2 x^4+e^5 \left (-12 x+6 x^2+4 x^3-2 x^4\right )\right )+\left (2 x+2 x^3+4 e^5 x^3+2 e^{10} x^3+2 e^{2-2 x} x^3+e^{1-x} \left (4 x^3+4 e^5 x^3\right )\right ) \log \left (1+x^2+2 e^5 x^2+e^{10} x^2+e^{2-2 x} x^2+e^{1-x} \left (2 x^2+2 e^5 x^2\right )\right )}{1+x^2+2 e^5 x^2+e^{10} x^2+e^{2-2 x} x^2+e^{1-x} \left (2 x^2+2 e^5 x^2\right )} \, dx=x^{2} \log {\left (x^{2} e^{2 - 2 x} + x^{2} + 2 x^{2} e^{5} + x^{2} e^{10} + \left (2 x^{2} + 2 x^{2} e^{5}\right ) e^{1 - x} + 1 \right )} - 6 \log {\left (x \right )} - 3 \log {\left (\left (2 + 2 e^{5}\right ) e^{1 - x} + e^{2 - 2 x} + \frac {x^{2} + 2 x^{2} e^{5} + x^{2} e^{10} + 1}{x^{2}} \right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 127 vs. \(2 (25) = 50\).
Time = 0.30 (sec) , antiderivative size = 127, normalized size of antiderivative = 4.70 \[ \int \frac {-6 x+2 x^3+e^{10} \left (-6 x+2 x^3\right )+e^5 \left (-12 x+4 x^3\right )+e^{2-2 x} \left (-6 x+6 x^2+2 x^3-2 x^4\right )+e^{1-x} \left (-12 x+6 x^2+4 x^3-2 x^4+e^5 \left (-12 x+6 x^2+4 x^3-2 x^4\right )\right )+\left (2 x+2 x^3+4 e^5 x^3+2 e^{10} x^3+2 e^{2-2 x} x^3+e^{1-x} \left (4 x^3+4 e^5 x^3\right )\right ) \log \left (1+x^2+2 e^5 x^2+e^{10} x^2+e^{2-2 x} x^2+e^{1-x} \left (2 x^2+2 e^5 x^2\right )\right )}{1+x^2+2 e^5 x^2+e^{10} x^2+e^{2-2 x} x^2+e^{1-x} \left (2 x^2+2 e^5 x^2\right )} \, dx=-2 \, x^{3} + x^{2} \log \left (2 \, x^{2} {\left (e^{6} + e\right )} e^{x} + x^{2} e^{2} + {\left (x^{2} {\left (e^{10} + 2 \, e^{5} + 1\right )} + 1\right )} e^{\left (2 \, x\right )}\right ) + 6 \, x - 3 \, \log \left (x^{2} {\left (e^{10} + 2 \, e^{5} + 1\right )} + 1\right ) - 3 \, \log \left (\frac {2 \, x^{2} {\left (e^{6} + e\right )} e^{x} + x^{2} e^{2} + {\left (x^{2} {\left (e^{10} + 2 \, e^{5} + 1\right )} + 1\right )} e^{\left (2 \, x\right )}}{x^{2} {\left (e^{10} + 2 \, e^{5} + 1\right )} + 1}\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 434 vs. \(2 (25) = 50\).
Time = 2.18 (sec) , antiderivative size = 434, normalized size of antiderivative = 16.07 \[ \int \frac {-6 x+2 x^3+e^{10} \left (-6 x+2 x^3\right )+e^5 \left (-12 x+4 x^3\right )+e^{2-2 x} \left (-6 x+6 x^2+2 x^3-2 x^4\right )+e^{1-x} \left (-12 x+6 x^2+4 x^3-2 x^4+e^5 \left (-12 x+6 x^2+4 x^3-2 x^4\right )\right )+\left (2 x+2 x^3+4 e^5 x^3+2 e^{10} x^3+2 e^{2-2 x} x^3+e^{1-x} \left (4 x^3+4 e^5 x^3\right )\right ) \log \left (1+x^2+2 e^5 x^2+e^{10} x^2+e^{2-2 x} x^2+e^{1-x} \left (2 x^2+2 e^5 x^2\right )\right )}{1+x^2+2 e^5 x^2+e^{10} x^2+e^{2-2 x} x^2+e^{1-x} \left (2 x^2+2 e^5 x^2\right )} \, dx={\left (x - 1\right )}^{2} \log \left ({\left (x - 1\right )}^{2} e^{10} + 2 \, {\left (x - 1\right )}^{2} e^{5} + 2 \, {\left (x - 1\right )}^{2} e^{\left (-x + 6\right )} + 2 \, {\left (x - 1\right )}^{2} e^{\left (-x + 1\right )} + {\left (x - 1\right )}^{2} e^{\left (-2 \, x + 2\right )} + {\left (x - 1\right )}^{2} + 2 \, {\left (x - 1\right )} e^{10} + 4 \, {\left (x - 1\right )} e^{5} + 4 \, {\left (x - 1\right )} e^{\left (-x + 6\right )} + 4 \, {\left (x - 1\right )} e^{\left (-x + 1\right )} + 2 \, {\left (x - 1\right )} e^{\left (-2 \, x + 2\right )} + 2 \, x + e^{10} + 2 \, e^{5} + 2 \, e^{\left (-x + 6\right )} + 2 \, e^{\left (-x + 1\right )} + e^{\left (-2 \, x + 2\right )}\right ) + 2 \, {\left (x - 1\right )} \log \left ({\left (x - 1\right )}^{2} e^{10} + 2 \, {\left (x - 1\right )}^{2} e^{5} + 2 \, {\left (x - 1\right )}^{2} e^{\left (-x + 6\right )} + 2 \, {\left (x - 1\right )}^{2} e^{\left (-x + 1\right )} + {\left (x - 1\right )}^{2} e^{\left (-2 \, x + 2\right )} + {\left (x - 1\right )}^{2} + 2 \, {\left (x - 1\right )} e^{10} + 4 \, {\left (x - 1\right )} e^{5} + 4 \, {\left (x - 1\right )} e^{\left (-x + 6\right )} + 4 \, {\left (x - 1\right )} e^{\left (-x + 1\right )} + 2 \, {\left (x - 1\right )} e^{\left (-2 \, x + 2\right )} + 2 \, x + e^{10} + 2 \, e^{5} + 2 \, e^{\left (-x + 6\right )} + 2 \, e^{\left (-x + 1\right )} + e^{\left (-2 \, x + 2\right )}\right ) - 2 \, \log \left ({\left (x - 1\right )}^{2} e^{10} + 2 \, {\left (x - 1\right )}^{2} e^{5} + 2 \, {\left (x - 1\right )}^{2} e^{\left (-x + 6\right )} + 2 \, {\left (x - 1\right )}^{2} e^{\left (-x + 1\right )} + {\left (x - 1\right )}^{2} e^{\left (-2 \, x + 2\right )} + {\left (x - 1\right )}^{2} + 2 \, {\left (x - 1\right )} e^{10} + 4 \, {\left (x - 1\right )} e^{5} + 4 \, {\left (x - 1\right )} e^{\left (-x + 6\right )} + 4 \, {\left (x - 1\right )} e^{\left (-x + 1\right )} + 2 \, {\left (x - 1\right )} e^{\left (-2 \, x + 2\right )} + 2 \, x + e^{10} + 2 \, e^{5} + 2 \, e^{\left (-x + 6\right )} + 2 \, e^{\left (-x + 1\right )} + e^{\left (-2 \, x + 2\right )}\right ) \]
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Time = 0.81 (sec) , antiderivative size = 119, normalized size of antiderivative = 4.41 \[ \int \frac {-6 x+2 x^3+e^{10} \left (-6 x+2 x^3\right )+e^5 \left (-12 x+4 x^3\right )+e^{2-2 x} \left (-6 x+6 x^2+2 x^3-2 x^4\right )+e^{1-x} \left (-12 x+6 x^2+4 x^3-2 x^4+e^5 \left (-12 x+6 x^2+4 x^3-2 x^4\right )\right )+\left (2 x+2 x^3+4 e^5 x^3+2 e^{10} x^3+2 e^{2-2 x} x^3+e^{1-x} \left (4 x^3+4 e^5 x^3\right )\right ) \log \left (1+x^2+2 e^5 x^2+e^{10} x^2+e^{2-2 x} x^2+e^{1-x} \left (2 x^2+2 e^5 x^2\right )\right )}{1+x^2+2 e^5 x^2+e^{10} x^2+e^{2-2 x} x^2+e^{1-x} \left (2 x^2+2 e^5 x^2\right )} \, dx=x^2\,\ln \left (2\,x^2\,{\mathrm {e}}^5+x^2\,{\mathrm {e}}^{10}+x^2+2\,x^2\,{\mathrm {e}}^{-x}\,\mathrm {e}+x^2\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^2+2\,x^2\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^6+1\right )-3\,\ln \left (2\,x^2\,{\mathrm {e}}^5+x^2\,{\mathrm {e}}^{10}+x^2+2\,x^2\,{\mathrm {e}}^{-x}\,\mathrm {e}+x^2\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^2+2\,x^2\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^6+1\right )-6\,\ln \left (x\right )-3\,\ln \left (\frac {1}{x^2}\right ) \]
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