Integrand size = 403, antiderivative size = 35 \[ \int \frac {\left (2 e^{e^x+x} x^4+12 x^5+\left (-12 x^5+6 x^6+e^{e^x} \left (-4 x^3+2 x^4\right )\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log \left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )+\left (\left (-2 e^{e^x} x^3-6 x^5\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (10 e^{e^x+x} x+30 e^x x^3\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log ^2\left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )}{\left (-e^{e^x} x^2-3 x^4\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (5 e^{e^x+x}+15 e^x x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx=x^2 \log ^2\left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right ) \]
Time = 0.35 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.00 \[ \int \frac {\left (2 e^{e^x+x} x^4+12 x^5+\left (-12 x^5+6 x^6+e^{e^x} \left (-4 x^3+2 x^4\right )\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log \left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )+\left (\left (-2 e^{e^x} x^3-6 x^5\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (10 e^{e^x+x} x+30 e^x x^3\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log ^2\left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )}{\left (-e^{e^x} x^2-3 x^4\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (5 e^{e^x+x}+15 e^x x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx=x^2 \log ^2\left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right ) \]
Integrate[((2*E^(E^x + x)*x^4 + 12*x^5 + (-12*x^5 + 6*x^6 + E^E^x*(-4*x^3 + 2*x^4))*Log[(E^E^x + 3*x^2)/3]*Log[Log[(E^E^x + 3*x^2)/3]])*Log[(x^2 - 5 *E^x*Log[Log[(E^E^x + 3*x^2)/3]])/(E^x*Log[Log[(E^E^x + 3*x^2)/3]])] + ((- 2*E^E^x*x^3 - 6*x^5)*Log[(E^E^x + 3*x^2)/3]*Log[Log[(E^E^x + 3*x^2)/3]] + (10*E^(E^x + x)*x + 30*E^x*x^3)*Log[(E^E^x + 3*x^2)/3]*Log[Log[(E^E^x + 3* x^2)/3]]^2)*Log[(x^2 - 5*E^x*Log[Log[(E^E^x + 3*x^2)/3]])/(E^x*Log[Log[(E^ E^x + 3*x^2)/3]])]^2)/((-(E^E^x*x^2) - 3*x^4)*Log[(E^E^x + 3*x^2)/3]*Log[L og[(E^E^x + 3*x^2)/3]] + (5*E^(E^x + x) + 15*E^x*x^2)*Log[(E^E^x + 3*x^2)/ 3]*Log[Log[(E^E^x + 3*x^2)/3]]^2),x]
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {\left (\left (30 e^x x^3+10 e^{x+e^x} x\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )+\left (-6 x^5-2 e^{e^x} x^3\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \log \left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )\right ) \log ^2\left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}\right )+\left (12 x^5+2 e^{x+e^x} x^4+\left (6 x^6-12 x^5+e^{e^x} \left (2 x^4-4 x^3\right )\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \log \left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )\right ) \log \left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}\right )}{\left (15 e^x x^2+5 e^{x+e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )+\left (-3 x^4-e^{e^x} x^2\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \log \left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) \left (-\left (\left (6 x+e^{x+e^x}\right ) x^3\right )-\left (3 x^2+e^{e^x}\right ) \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \left ((x-2) x^2-\left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right )\right )\right )}{\left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int -\frac {x \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) \left (x^3 \left (6 x+e^{x+e^x}\right )-\left (3 x^2+e^{e^x}\right ) \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \left ((2-x) x^2+\left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right )\right )\right )}{\left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -2 \int \frac {x \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) \left (x^3 \left (6 x+e^{x+e^x}\right )-\left (3 x^2+e^{e^x}\right ) \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \left ((2-x) x^2+\left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right )\right )\right )}{\left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (e^{e^x} x^3+15 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^3-30 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^2+30 \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^2+5 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x-10 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) x^3}{5 \left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}+\frac {\log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) \left (-e^{e^x} x^3-15 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) x^2-5 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right )\right ) x}{5 \left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) \left (\left (6 x+e^{x+e^x}\right ) x^3+\left (3 x^2+e^{e^x}\right ) \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \left ((x-2) x^2-\left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right )\right )\right )}{\left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (e^{e^x} x^3+15 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^3-30 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^2+30 \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^2+5 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x-10 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) x^3}{5 \left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}+\frac {\log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) \left (-e^{e^x} x^3-15 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) x^2-5 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right )\right ) x}{5 \left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) \left (\left (6 x+e^{x+e^x}\right ) x^3+\left (3 x^2+e^{e^x}\right ) \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \left ((x-2) x^2-\left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right )\right )\right )}{\left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (e^{e^x} x^3+15 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^3-30 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^2+30 \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^2+5 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x-10 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) x^3}{5 \left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}+\frac {\log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) \left (-e^{e^x} x^3-15 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) x^2-5 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right )\right ) x}{5 \left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) \left (\left (6 x+e^{x+e^x}\right ) x^3+\left (3 x^2+e^{e^x}\right ) \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \left ((x-2) x^2-\left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right )\right )\right )}{\left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (e^{e^x} x^3+15 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^3-30 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^2+30 \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^2+5 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x-10 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) x^3}{5 \left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}+\frac {\log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) \left (-e^{e^x} x^3-15 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) x^2-5 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right )\right ) x}{5 \left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) \left (\left (6 x+e^{x+e^x}\right ) x^3+\left (3 x^2+e^{e^x}\right ) \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \left ((x-2) x^2-\left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right )\right )\right )}{\left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (e^{e^x} x^3+15 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^3-30 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^2+30 \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^2+5 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x-10 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) x^3}{5 \left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}+\frac {\log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) \left (-e^{e^x} x^3-15 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) x^2-5 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right )\right ) x}{5 \left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) \left (\left (6 x+e^{x+e^x}\right ) x^3+\left (3 x^2+e^{e^x}\right ) \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \left ((x-2) x^2-\left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right )\right )\right )}{\left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (e^{e^x} x^3+15 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^3-30 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^2+30 \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^2+5 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x-10 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) x^3}{5 \left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}+\frac {\log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) \left (-e^{e^x} x^3-15 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) x^2-5 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right )\right ) x}{5 \left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) \left (\left (6 x+e^{x+e^x}\right ) x^3+\left (3 x^2+e^{e^x}\right ) \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \left ((x-2) x^2-\left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right )\right )\right )}{\left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (e^{e^x} x^3+15 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^3-30 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^2+30 \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^2+5 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x-10 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) x^3}{5 \left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}+\frac {\log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) \left (-e^{e^x} x^3-15 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) x^2-5 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right )\right ) x}{5 \left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) \left (\left (6 x+e^{x+e^x}\right ) x^3+\left (3 x^2+e^{e^x}\right ) \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \left ((x-2) x^2-\left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right )\right )\right )}{\left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (e^{e^x} x^3+15 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^3-30 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^2+30 \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^2+5 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x-10 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) x^3}{5 \left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}+\frac {\log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) \left (-e^{e^x} x^3-15 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) x^2-5 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right )\right ) x}{5 \left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) \left (\left (6 x+e^{x+e^x}\right ) x^3+\left (3 x^2+e^{e^x}\right ) \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \left ((x-2) x^2-\left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right )\right )\right )}{\left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (e^{e^x} x^3+15 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^3-30 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^2+30 \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^2+5 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x-10 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) x^3}{5 \left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}+\frac {\log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) \left (-e^{e^x} x^3-15 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) x^2-5 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right )\right ) x}{5 \left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) \left (\left (6 x+e^{x+e^x}\right ) x^3+\left (3 x^2+e^{e^x}\right ) \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \left ((x-2) x^2-\left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right )\right )\right )}{\left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (e^{e^x} x^3+15 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^3-30 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^2+30 \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^2+5 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x-10 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) x^3}{5 \left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}+\frac {\log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) \left (-e^{e^x} x^3-15 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) x^2-5 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right )\right ) x}{5 \left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) \left (\left (6 x+e^{x+e^x}\right ) x^3+\left (3 x^2+e^{e^x}\right ) \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \left ((x-2) x^2-\left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right )\right )\right )}{\left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (e^{e^x} x^3+15 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^3-30 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^2+30 \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^2+5 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x-10 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) x^3}{5 \left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}+\frac {\log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) \left (-e^{e^x} x^3-15 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) x^2-5 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right )\right ) x}{5 \left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) \left (\left (6 x+e^{x+e^x}\right ) x^3+\left (3 x^2+e^{e^x}\right ) \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \left ((x-2) x^2-\left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right )\right )\right )}{\left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (e^{e^x} x^3+15 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^3-30 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^2+30 \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^2+5 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x-10 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) x^3}{5 \left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}+\frac {\log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) \left (-e^{e^x} x^3-15 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) x^2-5 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right )\right ) x}{5 \left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) \left (\left (6 x+e^{x+e^x}\right ) x^3+\left (3 x^2+e^{e^x}\right ) \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \left ((x-2) x^2-\left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right )\right )\right )}{\left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (e^{e^x} x^3+15 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^3-30 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^2+30 \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^2+5 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x-10 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) x^3}{5 \left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}+\frac {\log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) \left (-e^{e^x} x^3-15 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) x^2-5 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right )\right ) x}{5 \left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) \left (\left (6 x+e^{x+e^x}\right ) x^3+\left (3 x^2+e^{e^x}\right ) \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \left ((x-2) x^2-\left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right )\right )\right )}{\left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\left (e^{e^x} x^3+15 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^3-30 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^2+30 \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x^2+5 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) x-10 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) x^3}{5 \left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \left (x^2-5 e^x \log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}+\frac {\log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) \left (-e^{e^x} x^3-15 \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right ) x^2-5 e^{e^x} \log \left (x^2+\frac {e^{e^x}}{3}\right ) \log ^2\left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right ) \log \left (\frac {e^{-x} x^2}{\log \left (\log \left (x^2+\frac {e^{e^x}}{3}\right )\right )}-5\right )\right ) x}{5 \left (3 x^2+e^{e^x}\right ) \log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (3 x^2+e^{e^x}\right )\right )\right )}\right )dx\) |
Int[((2*E^(E^x + x)*x^4 + 12*x^5 + (-12*x^5 + 6*x^6 + E^E^x*(-4*x^3 + 2*x^ 4))*Log[(E^E^x + 3*x^2)/3]*Log[Log[(E^E^x + 3*x^2)/3]])*Log[(x^2 - 5*E^x*L og[Log[(E^E^x + 3*x^2)/3]])/(E^x*Log[Log[(E^E^x + 3*x^2)/3]])] + ((-2*E^E^ x*x^3 - 6*x^5)*Log[(E^E^x + 3*x^2)/3]*Log[Log[(E^E^x + 3*x^2)/3]] + (10*E^ (E^x + x)*x + 30*E^x*x^3)*Log[(E^E^x + 3*x^2)/3]*Log[Log[(E^E^x + 3*x^2)/3 ]]^2)*Log[(x^2 - 5*E^x*Log[Log[(E^E^x + 3*x^2)/3]])/(E^x*Log[Log[(E^E^x + 3*x^2)/3]])]^2)/((-(E^E^x*x^2) - 3*x^4)*Log[(E^E^x + 3*x^2)/3]*Log[Log[(E^ E^x + 3*x^2)/3]] + (5*E^(E^x + x) + 15*E^x*x^2)*Log[(E^E^x + 3*x^2)/3]*Log [Log[(E^E^x + 3*x^2)/3]]^2),x]
3.25.27.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 0.50 (sec) , antiderivative size = 5397, normalized size of antiderivative = 154.20
\[\text {output too large to display}\]
int((((10*x*exp(x)*exp(exp(x))+30*exp(x)*x^3)*ln(1/3*exp(exp(x))+x^2)*ln(l n(1/3*exp(exp(x))+x^2))^2+(-2*x^3*exp(exp(x))-6*x^5)*ln(1/3*exp(exp(x))+x^ 2)*ln(ln(1/3*exp(exp(x))+x^2)))*ln((-5*exp(x)*ln(ln(1/3*exp(exp(x))+x^2))+ x^2)/exp(x)/ln(ln(1/3*exp(exp(x))+x^2)))^2+(((2*x^4-4*x^3)*exp(exp(x))+6*x ^6-12*x^5)*ln(1/3*exp(exp(x))+x^2)*ln(ln(1/3*exp(exp(x))+x^2))+2*x^4*exp(x )*exp(exp(x))+12*x^5)*ln((-5*exp(x)*ln(ln(1/3*exp(exp(x))+x^2))+x^2)/exp(x )/ln(ln(1/3*exp(exp(x))+x^2))))/((5*exp(x)*exp(exp(x))+15*exp(x)*x^2)*ln(1 /3*exp(exp(x))+x^2)*ln(ln(1/3*exp(exp(x))+x^2))^2+(-exp(exp(x))*x^2-3*x^4) *ln(1/3*exp(exp(x))+x^2)*ln(ln(1/3*exp(exp(x))+x^2))),x)
Leaf count of result is larger than twice the leaf count of optimal. 64 vs. \(2 (30) = 60\).
Time = 0.28 (sec) , antiderivative size = 64, normalized size of antiderivative = 1.83 \[ \int \frac {\left (2 e^{e^x+x} x^4+12 x^5+\left (-12 x^5+6 x^6+e^{e^x} \left (-4 x^3+2 x^4\right )\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log \left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )+\left (\left (-2 e^{e^x} x^3-6 x^5\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (10 e^{e^x+x} x+30 e^x x^3\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log ^2\left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )}{\left (-e^{e^x} x^2-3 x^4\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (5 e^{e^x+x}+15 e^x x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx=x^{2} \log \left (\frac {{\left (x^{2} - 5 \, e^{x} \log \left (\log \left (\frac {1}{3} \, {\left (3 \, x^{2} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )\right )\right )} e^{\left (-x\right )}}{\log \left (\log \left (\frac {1}{3} \, {\left (3 \, x^{2} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )\right )}\right )^{2} \]
integrate((((10*x*exp(x)*exp(exp(x))+30*exp(x)*x^3)*log(1/3*exp(exp(x))+x^ 2)*log(log(1/3*exp(exp(x))+x^2))^2+(-2*x^3*exp(exp(x))-6*x^5)*log(1/3*exp( exp(x))+x^2)*log(log(1/3*exp(exp(x))+x^2)))*log((-5*exp(x)*log(log(1/3*exp (exp(x))+x^2))+x^2)/exp(x)/log(log(1/3*exp(exp(x))+x^2)))^2+(((2*x^4-4*x^3 )*exp(exp(x))+6*x^6-12*x^5)*log(1/3*exp(exp(x))+x^2)*log(log(1/3*exp(exp(x ))+x^2))+2*x^4*exp(x)*exp(exp(x))+12*x^5)*log((-5*exp(x)*log(log(1/3*exp(e xp(x))+x^2))+x^2)/exp(x)/log(log(1/3*exp(exp(x))+x^2))))/((5*exp(x)*exp(ex p(x))+15*exp(x)*x^2)*log(1/3*exp(exp(x))+x^2)*log(log(1/3*exp(exp(x))+x^2) )^2+(-exp(exp(x))*x^2-3*x^4)*log(1/3*exp(exp(x))+x^2)*log(log(1/3*exp(exp( x))+x^2))),x, algorithm=\
x^2*log((x^2 - 5*e^x*log(log(1/3*(3*x^2*e^x + e^(x + e^x))*e^(-x))))*e^(-x )/log(log(1/3*(3*x^2*e^x + e^(x + e^x))*e^(-x))))^2
Timed out. \[ \int \frac {\left (2 e^{e^x+x} x^4+12 x^5+\left (-12 x^5+6 x^6+e^{e^x} \left (-4 x^3+2 x^4\right )\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log \left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )+\left (\left (-2 e^{e^x} x^3-6 x^5\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (10 e^{e^x+x} x+30 e^x x^3\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log ^2\left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )}{\left (-e^{e^x} x^2-3 x^4\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (5 e^{e^x+x}+15 e^x x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx=\text {Timed out} \]
integrate((((10*x*exp(x)*exp(exp(x))+30*exp(x)*x**3)*ln(1/3*exp(exp(x))+x* *2)*ln(ln(1/3*exp(exp(x))+x**2))**2+(-2*x**3*exp(exp(x))-6*x**5)*ln(1/3*ex p(exp(x))+x**2)*ln(ln(1/3*exp(exp(x))+x**2)))*ln((-5*exp(x)*ln(ln(1/3*exp( exp(x))+x**2))+x**2)/exp(x)/ln(ln(1/3*exp(exp(x))+x**2)))**2+(((2*x**4-4*x **3)*exp(exp(x))+6*x**6-12*x**5)*ln(1/3*exp(exp(x))+x**2)*ln(ln(1/3*exp(ex p(x))+x**2))+2*x**4*exp(x)*exp(exp(x))+12*x**5)*ln((-5*exp(x)*ln(ln(1/3*ex p(exp(x))+x**2))+x**2)/exp(x)/ln(ln(1/3*exp(exp(x))+x**2))))/((5*exp(x)*ex p(exp(x))+15*exp(x)*x**2)*ln(1/3*exp(exp(x))+x**2)*ln(ln(1/3*exp(exp(x))+x **2))**2+(-exp(exp(x))*x**2-3*x**4)*ln(1/3*exp(exp(x))+x**2)*ln(ln(1/3*exp (exp(x))+x**2))),x)
Leaf count of result is larger than twice the leaf count of optimal. 132 vs. \(2 (30) = 60\).
Time = 0.97 (sec) , antiderivative size = 132, normalized size of antiderivative = 3.77 \[ \int \frac {\left (2 e^{e^x+x} x^4+12 x^5+\left (-12 x^5+6 x^6+e^{e^x} \left (-4 x^3+2 x^4\right )\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log \left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )+\left (\left (-2 e^{e^x} x^3-6 x^5\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (10 e^{e^x+x} x+30 e^x x^3\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log ^2\left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )}{\left (-e^{e^x} x^2-3 x^4\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (5 e^{e^x+x}+15 e^x x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx=x^{4} + x^{2} \log \left (x^{2} - 5 \, e^{x} \log \left (-\log \left (3\right ) + \log \left (3 \, x^{2} + e^{\left (e^{x}\right )}\right )\right )\right )^{2} + 2 \, x^{3} \log \left (\log \left (-\log \left (3\right ) + \log \left (3 \, x^{2} + e^{\left (e^{x}\right )}\right )\right )\right ) + x^{2} \log \left (\log \left (-\log \left (3\right ) + \log \left (3 \, x^{2} + e^{\left (e^{x}\right )}\right )\right )\right )^{2} - 2 \, {\left (x^{3} + x^{2} \log \left (\log \left (-\log \left (3\right ) + \log \left (3 \, x^{2} + e^{\left (e^{x}\right )}\right )\right )\right )\right )} \log \left (x^{2} - 5 \, e^{x} \log \left (-\log \left (3\right ) + \log \left (3 \, x^{2} + e^{\left (e^{x}\right )}\right )\right )\right ) \]
integrate((((10*x*exp(x)*exp(exp(x))+30*exp(x)*x^3)*log(1/3*exp(exp(x))+x^ 2)*log(log(1/3*exp(exp(x))+x^2))^2+(-2*x^3*exp(exp(x))-6*x^5)*log(1/3*exp( exp(x))+x^2)*log(log(1/3*exp(exp(x))+x^2)))*log((-5*exp(x)*log(log(1/3*exp (exp(x))+x^2))+x^2)/exp(x)/log(log(1/3*exp(exp(x))+x^2)))^2+(((2*x^4-4*x^3 )*exp(exp(x))+6*x^6-12*x^5)*log(1/3*exp(exp(x))+x^2)*log(log(1/3*exp(exp(x ))+x^2))+2*x^4*exp(x)*exp(exp(x))+12*x^5)*log((-5*exp(x)*log(log(1/3*exp(e xp(x))+x^2))+x^2)/exp(x)/log(log(1/3*exp(exp(x))+x^2))))/((5*exp(x)*exp(ex p(x))+15*exp(x)*x^2)*log(1/3*exp(exp(x))+x^2)*log(log(1/3*exp(exp(x))+x^2) )^2+(-exp(exp(x))*x^2-3*x^4)*log(1/3*exp(exp(x))+x^2)*log(log(1/3*exp(exp( x))+x^2))),x, algorithm=\
x^4 + x^2*log(x^2 - 5*e^x*log(-log(3) + log(3*x^2 + e^(e^x))))^2 + 2*x^3*l og(log(-log(3) + log(3*x^2 + e^(e^x)))) + x^2*log(log(-log(3) + log(3*x^2 + e^(e^x))))^2 - 2*(x^3 + x^2*log(log(-log(3) + log(3*x^2 + e^(e^x)))))*lo g(x^2 - 5*e^x*log(-log(3) + log(3*x^2 + e^(e^x))))
Leaf count of result is larger than twice the leaf count of optimal. 211 vs. \(2 (30) = 60\).
Time = 0.56 (sec) , antiderivative size = 211, normalized size of antiderivative = 6.03 \[ \int \frac {\left (2 e^{e^x+x} x^4+12 x^5+\left (-12 x^5+6 x^6+e^{e^x} \left (-4 x^3+2 x^4\right )\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log \left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )+\left (\left (-2 e^{e^x} x^3-6 x^5\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (10 e^{e^x+x} x+30 e^x x^3\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log ^2\left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )}{\left (-e^{e^x} x^2-3 x^4\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (5 e^{e^x+x}+15 e^x x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx=x^{4} - 2 \, x^{3} \log \left (x^{2} - 5 \, e^{x} \log \left (-\log \left (3\right ) + \log \left ({\left (3 \, x^{2} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )\right )\right ) + x^{2} \log \left (x^{2} - 5 \, e^{x} \log \left (-\log \left (3\right ) + \log \left ({\left (3 \, x^{2} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )\right )\right )^{2} + 2 \, x^{3} \log \left (\log \left (-\log \left (3\right ) + \log \left ({\left (3 \, x^{2} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )\right )\right ) - 2 \, x^{2} \log \left (x^{2} - 5 \, e^{x} \log \left (-\log \left (3\right ) + \log \left ({\left (3 \, x^{2} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )\right )\right ) \log \left (\log \left (-\log \left (3\right ) + \log \left ({\left (3 \, x^{2} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )\right )\right ) + x^{2} \log \left (\log \left (-\log \left (3\right ) + \log \left ({\left (3 \, x^{2} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )\right )\right )^{2} \]
integrate((((10*x*exp(x)*exp(exp(x))+30*exp(x)*x^3)*log(1/3*exp(exp(x))+x^ 2)*log(log(1/3*exp(exp(x))+x^2))^2+(-2*x^3*exp(exp(x))-6*x^5)*log(1/3*exp( exp(x))+x^2)*log(log(1/3*exp(exp(x))+x^2)))*log((-5*exp(x)*log(log(1/3*exp (exp(x))+x^2))+x^2)/exp(x)/log(log(1/3*exp(exp(x))+x^2)))^2+(((2*x^4-4*x^3 )*exp(exp(x))+6*x^6-12*x^5)*log(1/3*exp(exp(x))+x^2)*log(log(1/3*exp(exp(x ))+x^2))+2*x^4*exp(x)*exp(exp(x))+12*x^5)*log((-5*exp(x)*log(log(1/3*exp(e xp(x))+x^2))+x^2)/exp(x)/log(log(1/3*exp(exp(x))+x^2))))/((5*exp(x)*exp(ex p(x))+15*exp(x)*x^2)*log(1/3*exp(exp(x))+x^2)*log(log(1/3*exp(exp(x))+x^2) )^2+(-exp(exp(x))*x^2-3*x^4)*log(1/3*exp(exp(x))+x^2)*log(log(1/3*exp(exp( x))+x^2))),x, algorithm=\
x^4 - 2*x^3*log(x^2 - 5*e^x*log(-log(3) + log((3*x^2*e^x + e^(x + e^x))*e^ (-x)))) + x^2*log(x^2 - 5*e^x*log(-log(3) + log((3*x^2*e^x + e^(x + e^x))* e^(-x))))^2 + 2*x^3*log(log(-log(3) + log((3*x^2*e^x + e^(x + e^x))*e^(-x) ))) - 2*x^2*log(x^2 - 5*e^x*log(-log(3) + log((3*x^2*e^x + e^(x + e^x))*e^ (-x))))*log(log(-log(3) + log((3*x^2*e^x + e^(x + e^x))*e^(-x)))) + x^2*lo g(log(-log(3) + log((3*x^2*e^x + e^(x + e^x))*e^(-x))))^2
Time = 14.76 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.29 \[ \int \frac {\left (2 e^{e^x+x} x^4+12 x^5+\left (-12 x^5+6 x^6+e^{e^x} \left (-4 x^3+2 x^4\right )\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log \left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )+\left (\left (-2 e^{e^x} x^3-6 x^5\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (10 e^{e^x+x} x+30 e^x x^3\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log ^2\left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )}{\left (-e^{e^x} x^2-3 x^4\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (5 e^{e^x+x}+15 e^x x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx=x^2\,{\ln \left (-\frac {5\,\ln \left (\ln \left (\frac {{\mathrm {e}}^{{\mathrm {e}}^x}}{3}+x^2\right )\right )-x^2\,{\mathrm {e}}^{-x}}{\ln \left (\ln \left (\frac {{\mathrm {e}}^{{\mathrm {e}}^x}}{3}+x^2\right )\right )}\right )}^2 \]
int(-(log((exp(-x)*(x^2 - 5*exp(x)*log(log(exp(exp(x))/3 + x^2))))/log(log (exp(exp(x))/3 + x^2)))*(12*x^5 + 2*x^4*exp(exp(x))*exp(x) - log(exp(exp(x ))/3 + x^2)*log(log(exp(exp(x))/3 + x^2))*(exp(exp(x))*(4*x^3 - 2*x^4) + 1 2*x^5 - 6*x^6)) + log((exp(-x)*(x^2 - 5*exp(x)*log(log(exp(exp(x))/3 + x^2 ))))/log(log(exp(exp(x))/3 + x^2)))^2*(log(exp(exp(x))/3 + x^2)*log(log(ex p(exp(x))/3 + x^2))^2*(30*x^3*exp(x) + 10*x*exp(exp(x))*exp(x)) - log(exp( exp(x))/3 + x^2)*log(log(exp(exp(x))/3 + x^2))*(2*x^3*exp(exp(x)) + 6*x^5) ))/(log(exp(exp(x))/3 + x^2)*log(log(exp(exp(x))/3 + x^2))*(x^2*exp(exp(x) ) + 3*x^4) - log(exp(exp(x))/3 + x^2)*log(log(exp(exp(x))/3 + x^2))^2*(15* x^2*exp(x) + 5*exp(exp(x))*exp(x))),x)