Integrand size = 317, antiderivative size = 33 \[ \int \frac {e^{e^{\frac {-\frac {(-4+x)^2 x}{e^4}+x^2-\frac {2 (-4+x) x^2}{e^2}-x^3}{1+\frac {(-4+x)^2 x}{e^4}-x^2+\frac {2 (-4+x) x^2}{e^2}+x^3}}+\frac {-\frac {(-4+x)^2 x}{e^4}+x^2-\frac {2 (-4+x) x^2}{e^2}-x^3}{1+\frac {(-4+x)^2 x}{e^4}-x^2+\frac {2 (-4+x) x^2}{e^2}+x^3}} \left (8 x-14 x^2+3 x^3+\frac {(-4+x)^2 (-4+3 x)}{e^4}+\frac {(-4+x) \left (-16 x+6 x^2\right )}{e^2}\right )}{-4+x+8 x^2-10 x^3-2 x^4+9 x^5-6 x^6+x^7+\frac {(-4+x)^4 \left (-4 x^2+x^3\right )}{e^8}+\frac {(-4+x)^3 \left (-16 x^3+4 x^4\right )}{e^6}+\frac {(-4+x)^2 \left (-8 x+2 x^2+8 x^3-26 x^4+6 x^5\right )}{e^4}+\frac {(-4+x) \left (-16 x^2+4 x^3+16 x^4-20 x^5+4 x^6\right )}{e^2}} \, dx=1-e^{e^{\frac {x}{-x+\frac {1}{x-\left (\frac {-4+x}{e^2}+x\right )^2}}}} \]
Time = 0.40 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.42 \[ \int \frac {e^{e^{\frac {-\frac {(-4+x)^2 x}{e^4}+x^2-\frac {2 (-4+x) x^2}{e^2}-x^3}{1+\frac {(-4+x)^2 x}{e^4}-x^2+\frac {2 (-4+x) x^2}{e^2}+x^3}}+\frac {-\frac {(-4+x)^2 x}{e^4}+x^2-\frac {2 (-4+x) x^2}{e^2}-x^3}{1+\frac {(-4+x)^2 x}{e^4}-x^2+\frac {2 (-4+x) x^2}{e^2}+x^3}} \left (8 x-14 x^2+3 x^3+\frac {(-4+x)^2 (-4+3 x)}{e^4}+\frac {(-4+x) \left (-16 x+6 x^2\right )}{e^2}\right )}{-4+x+8 x^2-10 x^3-2 x^4+9 x^5-6 x^6+x^7+\frac {(-4+x)^4 \left (-4 x^2+x^3\right )}{e^8}+\frac {(-4+x)^3 \left (-16 x^3+4 x^4\right )}{e^6}+\frac {(-4+x)^2 \left (-8 x+2 x^2+8 x^3-26 x^4+6 x^5\right )}{e^4}+\frac {(-4+x) \left (-16 x^2+4 x^3+16 x^4-20 x^5+4 x^6\right )}{e^2}} \, dx=-e^{e^{-1+\frac {e^4}{(-4+x)^2 x+2 e^2 (-4+x) x^2+e^4 \left (1-x^2+x^3\right )}}} \]
Integrate[(E^(E^((-(((-4 + x)^2*x)/E^4) + x^2 - (2*(-4 + x)*x^2)/E^2 - x^3 )/(1 + ((-4 + x)^2*x)/E^4 - x^2 + (2*(-4 + x)*x^2)/E^2 + x^3)) + (-(((-4 + x)^2*x)/E^4) + x^2 - (2*(-4 + x)*x^2)/E^2 - x^3)/(1 + ((-4 + x)^2*x)/E^4 - x^2 + (2*(-4 + x)*x^2)/E^2 + x^3))*(8*x - 14*x^2 + 3*x^3 + ((-4 + x)^2*( -4 + 3*x))/E^4 + ((-4 + x)*(-16*x + 6*x^2))/E^2))/(-4 + x + 8*x^2 - 10*x^3 - 2*x^4 + 9*x^5 - 6*x^6 + x^7 + ((-4 + x)^4*(-4*x^2 + x^3))/E^8 + ((-4 + x)^3*(-16*x^3 + 4*x^4))/E^6 + ((-4 + x)^2*(-8*x + 2*x^2 + 8*x^3 - 26*x^4 + 6*x^5))/E^4 + ((-4 + x)*(-16*x^2 + 4*x^3 + 16*x^4 - 20*x^5 + 4*x^6))/E^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.
| \(\displaystyle \int \frac {\left (3 x^3-14 x^2+\frac {(x-4) \left (6 x^2-16 x\right )}{e^2}+8 x+\frac {(x-4)^2 (3 x-4)}{e^4}\right ) \exp \left (\exp \left (\frac {-x^3-\frac {2 (x-4) x^2}{e^2}+x^2-\frac {(x-4)^2 x}{e^4}}{x^3+\frac {2 (x-4) x^2}{e^2}-x^2+\frac {(x-4)^2 x}{e^4}+1}\right )+\frac {-x^3-\frac {2 (x-4) x^2}{e^2}+x^2-\frac {(x-4)^2 x}{e^4}}{x^3+\frac {2 (x-4) x^2}{e^2}-x^2+\frac {(x-4)^2 x}{e^4}+1}\right )}{x^7-6 x^6+9 x^5-2 x^4-10 x^3+8 x^2+\frac {(x-4)^3 \left (4 x^4-16 x^3\right )}{e^6}+\frac {(x-4)^4 \left (x^3-4 x^2\right )}{e^8}+\frac {(x-4)^2 \left (6 x^5-26 x^4+8 x^3+2 x^2-8 x\right )}{e^4}+\frac {(x-4) \left (4 x^6-20 x^5+16 x^4+4 x^3-16 x^2\right )}{e^2}+x-4} \, dx\) |
| \(\Big \downarrow \) 2457 |
| \(\displaystyle \int \frac {\left (\left (3 e^4+6 e^6+3 e^8\right ) x^2+\left (-16 e^4-16 e^6-2 e^8\right ) x+16 e^4\right ) \exp \left (\exp \left (\frac {-x^3-\frac {2 (x-4) x^2}{e^2}+x^2-\frac {(x-4)^2 x}{e^4}}{x^3+\frac {2 (x-4) x^2}{e^2}-x^2+\frac {(x-4)^2 x}{e^4}+1}\right )+\frac {-x^3-\frac {2 (x-4) x^2}{e^2}+x^2-\frac {(x-4)^2 x}{e^4}}{x^3+\frac {2 (x-4) x^2}{e^2}-x^2+\frac {(x-4)^2 x}{e^4}+1}\right )}{\left (1+4 e^2+6 e^4+4 e^6+e^8\right ) x^6+\left (-16-48 e^2-50 e^4-20 e^6-2 e^8\right ) x^5+\left (96+192 e^2+112 e^4+16 e^6+e^8\right ) x^4+\left (-256-256 e^2-30 e^4+4 e^6+2 e^8\right ) x^3+\left (256-16 e^4-16 e^6-2 e^8\right ) x^2+32 e^4 x+e^8}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int \frac {\left (\left (3 e^4+6 e^6+3 e^8\right ) x^2+\left (-16 e^4-16 e^6-2 e^8\right ) x+16 e^4\right ) \exp \left (\exp \left (\frac {-x^3-\frac {2 (x-4) x^2}{e^2}+x^2-\frac {(x-4)^2 x}{e^4}}{x^3+\frac {2 (x-4) x^2}{e^2}-x^2+\frac {(x-4)^2 x}{e^4}+1}\right )+\frac {-x^3-\frac {2 (x-4) x^2}{e^2}+x^2-\frac {(x-4)^2 x}{e^4}}{x^3+\frac {2 (x-4) x^2}{e^2}-x^2+\frac {(x-4)^2 x}{e^4}+1}\right )}{\left (e^4 x^3+2 e^2 x^3+x^3-e^4 x^2-8 e^2 x^2-8 x^2+16 x+e^4\right )^2}dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {\left (\left (3 e^4+6 e^6+3 e^8\right ) x^2+\left (-16 e^4-16 e^6-2 e^8\right ) x+16 e^4\right ) \exp \left (\exp \left (\frac {-x^3-\frac {2 (x-4) x^2}{e^2}+x^2-\frac {(x-4)^2 x}{e^4}}{x^3+\frac {2 (x-4) x^2}{e^2}-x^2+\frac {(x-4)^2 x}{e^4}+1}\right )+\frac {-x^3-\frac {2 (x-4) x^2}{e^2}+x^2-\frac {(x-4)^2 x}{e^4}}{x^3+\frac {2 (x-4) x^2}{e^2}-x^2+\frac {(x-4)^2 x}{e^4}+1}\right )}{\left (e^4 x^3+2 e^2 x^3+x^3+\left (-8-8 e^2\right ) x^2-e^4 x^2+16 x+e^4\right )^2}dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {\left (\left (3 e^4+6 e^6+3 e^8\right ) x^2+\left (-16 e^4-16 e^6-2 e^8\right ) x+16 e^4\right ) \exp \left (\exp \left (\frac {-x^3-\frac {2 (x-4) x^2}{e^2}+x^2-\frac {(x-4)^2 x}{e^4}}{x^3+\frac {2 (x-4) x^2}{e^2}-x^2+\frac {(x-4)^2 x}{e^4}+1}\right )+\frac {-x^3-\frac {2 (x-4) x^2}{e^2}+x^2-\frac {(x-4)^2 x}{e^4}}{x^3+\frac {2 (x-4) x^2}{e^2}-x^2+\frac {(x-4)^2 x}{e^4}+1}\right )}{\left (e^4 x^3+2 e^2 x^3+x^3+\left (-8-8 e^2-e^4\right ) x^2+16 x+e^4\right )^2}dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {\left (\left (3 e^4+6 e^6+3 e^8\right ) x^2+\left (-16 e^4-16 e^6-2 e^8\right ) x+16 e^4\right ) \exp \left (\exp \left (\frac {-x^3-\frac {2 (x-4) x^2}{e^2}+x^2-\frac {(x-4)^2 x}{e^4}}{x^3+\frac {2 (x-4) x^2}{e^2}-x^2+\frac {(x-4)^2 x}{e^4}+1}\right )+\frac {-x^3-\frac {2 (x-4) x^2}{e^2}+x^2-\frac {(x-4)^2 x}{e^4}}{x^3+\frac {2 (x-4) x^2}{e^2}-x^2+\frac {(x-4)^2 x}{e^4}+1}\right )}{\left (\left (1+2 e^2\right ) x^3+e^4 x^3+\left (-8-8 e^2-e^4\right ) x^2+16 x+e^4\right )^2}dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {\left (\left (3 e^4+6 e^6+3 e^8\right ) x^2+\left (-16 e^4-16 e^6-2 e^8\right ) x+16 e^4\right ) \exp \left (\exp \left (\frac {-x^3-\frac {2 (x-4) x^2}{e^2}+x^2-\frac {(x-4)^2 x}{e^4}}{x^3+\frac {2 (x-4) x^2}{e^2}-x^2+\frac {(x-4)^2 x}{e^4}+1}\right )+\frac {-x^3-\frac {2 (x-4) x^2}{e^2}+x^2-\frac {(x-4)^2 x}{e^4}}{x^3+\frac {2 (x-4) x^2}{e^2}-x^2+\frac {(x-4)^2 x}{e^4}+1}\right )}{\left (\left (1+2 e^2+e^4\right ) x^3+\left (-8-8 e^2-e^4\right ) x^2+16 x+e^4\right )^2}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {\left (3 e^4 \left (1+e^2\right )^2 x^2-2 e^4 \left (8+8 e^2+e^4\right ) x+16 e^4\right ) \exp \left (\exp \left (\frac {-x^3-\frac {2 (x-4) x^2}{e^2}+x^2-\frac {(x-4)^2 x}{e^4}}{x^3+\frac {2 (x-4) x^2}{e^2}-x^2+\frac {(x-4)^2 x}{e^4}+1}\right )+\frac {-x^3-\frac {2 (x-4) x^2}{e^2}+x^2-\frac {(x-4)^2 x}{e^4}}{x^3+\frac {2 (x-4) x^2}{e^2}-x^2+\frac {(x-4)^2 x}{e^4}+1}\right )}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {3 \left (1+e^2\right )^2 x^2 \exp \left (\exp \left (\frac {-x^3-\frac {2 (x-4) x^2}{e^2}+x^2-\frac {(x-4)^2 x}{e^4}}{x^3+\frac {2 (x-4) x^2}{e^2}-x^2+\frac {(x-4)^2 x}{e^4}+1}\right )+\frac {-x^3-\frac {2 (x-4) x^2}{e^2}+x^2-\frac {(x-4)^2 x}{e^4}}{x^3+\frac {2 (x-4) x^2}{e^2}-x^2+\frac {(x-4)^2 x}{e^4}+1}+4\right )}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}+\frac {2 \left (-8-8 e^2-e^4\right ) x \exp \left (\exp \left (\frac {-x^3-\frac {2 (x-4) x^2}{e^2}+x^2-\frac {(x-4)^2 x}{e^4}}{x^3+\frac {2 (x-4) x^2}{e^2}-x^2+\frac {(x-4)^2 x}{e^4}+1}\right )+\frac {-x^3-\frac {2 (x-4) x^2}{e^2}+x^2-\frac {(x-4)^2 x}{e^4}}{x^3+\frac {2 (x-4) x^2}{e^2}-x^2+\frac {(x-4)^2 x}{e^4}+1}+4\right )}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}+\frac {16 \exp \left (\exp \left (\frac {-x^3-\frac {2 (x-4) x^2}{e^2}+x^2-\frac {(x-4)^2 x}{e^4}}{x^3+\frac {2 (x-4) x^2}{e^2}-x^2+\frac {(x-4)^2 x}{e^4}+1}\right )+\frac {-x^3-\frac {2 (x-4) x^2}{e^2}+x^2-\frac {(x-4)^2 x}{e^4}}{x^3+\frac {2 (x-4) x^2}{e^2}-x^2+\frac {(x-4)^2 x}{e^4}+1}+4\right )}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (3 \left (1+e^2\right )^2 x^2-2 \left (8+8 e^2+e^4\right ) x+16\right ) \exp \left (\frac {\left (2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+x (x-4)^2\right ) \exp \left (-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+x (x-4)^2}\right )-e^4 x^3-2 e^2 (x-4) x^2+e^4 x^2+4 \left (2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+x (x-4)^2\right )-(x-4)^2 x}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}\right )}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {3 \left (1+e^2\right )^2 x^2 \exp \left (\frac {\left (2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+x (x-4)^2\right ) \exp \left (-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+x (x-4)^2}\right )-e^4 x^3-2 e^2 (x-4) x^2+e^4 x^2+4 \left (2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+x (x-4)^2\right )-(x-4)^2 x}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}\right )}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}+\frac {2 \left (-8-8 e^2-e^4\right ) x \exp \left (\frac {\left (2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+x (x-4)^2\right ) \exp \left (-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+x (x-4)^2}\right )-e^4 x^3-2 e^2 (x-4) x^2+e^4 x^2+4 \left (2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+x (x-4)^2\right )-(x-4)^2 x}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}\right )}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}+\frac {16 \exp \left (\frac {\left (2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+x (x-4)^2\right ) \exp \left (-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+x (x-4)^2}\right )-e^4 x^3-2 e^2 (x-4) x^2+e^4 x^2+4 \left (2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+x (x-4)^2\right )-(x-4)^2 x}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}\right )}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (3 \left (1+e^2\right )^2 x^2-2 \left (8+8 e^2+e^4\right ) x+16\right ) \exp \left (\frac {\exp \left (-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}\right ) \left (3 x (x-4)^2 \exp \left (\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+x (x-4)^2}\right )+6 x^2 (x-4) \exp \left (\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+x (x-4)^2}+2\right )+\left (3 x^3-3 x^2+4\right ) \exp \left (\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+x (x-4)^2}+4\right )+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+x (x-4)^2\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}\right )}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {3 e^{\frac {e^{-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (3 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{x (x-4)^2+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )}} x (x-4)^2+x (x-4)^2+6 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{x (x-4)^2+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )}+2} x^2 (x-4)+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{x (x-4)^2+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )}+4} \left (3 x^3-3 x^2+4\right )\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (1+e^2\right )^2 x^2}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}+\frac {2 e^{\frac {e^{-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (3 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{x (x-4)^2+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )}} x (x-4)^2+x (x-4)^2+6 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{x (x-4)^2+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )}+2} x^2 (x-4)+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{x (x-4)^2+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )}+4} \left (3 x^3-3 x^2+4\right )\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (-8-8 e^2-e^4\right ) x}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}+\frac {16 e^{\frac {e^{-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (3 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{x (x-4)^2+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )}} x (x-4)^2+x (x-4)^2+6 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{x (x-4)^2+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )}+2} x^2 (x-4)+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{x (x-4)^2+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )}+4} \left (3 x^3-3 x^2+4\right )\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}}}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (3 \left (1+e^2\right )^2 x^2-2 \left (8+8 e^2+e^4\right ) x+16\right ) \exp \left (\frac {\exp \left (-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}\right ) \left (3 x (x-4)^2 \exp \left (\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}\right )+6 x^2 (x-4) \exp \left (\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2\right )+\left (3 x^3-3 x^2+4\right ) \exp \left (\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4\right )+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+x (x-4)^2\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}\right )}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {3 e^{\frac {e^{-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (3 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} x (x-4)^2+x (x-4)^2+6 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2} x^2 (x-4)+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4} \left (3 x^3-3 x^2+4\right )\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (1+e^2\right )^2 x^2}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}+\frac {2 e^{\frac {e^{-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (3 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} x (x-4)^2+x (x-4)^2+6 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2} x^2 (x-4)+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4} \left (3 x^3-3 x^2+4\right )\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (-8-8 e^2-e^4\right ) x}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}+\frac {16 e^{\frac {e^{-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (3 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} x (x-4)^2+x (x-4)^2+6 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2} x^2 (x-4)+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4} \left (3 x^3-3 x^2+4\right )\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}}}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (3 \left (1+e^2\right )^2 x^2-2 \left (8+8 e^2+e^4\right ) x+16\right ) \exp \left (\frac {\exp \left (-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}\right ) \left (3 x (x-4)^2 \exp \left (\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}\right )+6 x^2 (x-4) \exp \left (\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2\right )+\left (3 x^3-3 x^2+4\right ) \exp \left (\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4\right )+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+x (x-4)^2\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}\right )}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {3 e^{\frac {e^{-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (3 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} x (x-4)^2+x (x-4)^2+6 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2} x^2 (x-4)+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4} \left (3 x^3-3 x^2+4\right )\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (1+e^2\right )^2 x^2}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}+\frac {2 e^{\frac {e^{-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (3 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} x (x-4)^2+x (x-4)^2+6 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2} x^2 (x-4)+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4} \left (3 x^3-3 x^2+4\right )\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (-8-8 e^2-e^4\right ) x}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}+\frac {16 e^{\frac {e^{-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (3 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} x (x-4)^2+x (x-4)^2+6 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2} x^2 (x-4)+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4} \left (3 x^3-3 x^2+4\right )\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}}}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (3 \left (1+e^2\right )^2 x^2-2 \left (8+8 e^2+e^4\right ) x+16\right ) \exp \left (\frac {\exp \left (-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}\right ) \left (3 x (x-4)^2 \exp \left (\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}\right )+6 x^2 (x-4) \exp \left (\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2\right )+\left (3 x^3-3 x^2+4\right ) \exp \left (\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4\right )+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+x (x-4)^2\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}\right )}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {3 e^{\frac {e^{-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (3 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} x (x-4)^2+x (x-4)^2+6 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2} x^2 (x-4)+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4} \left (3 x^3-3 x^2+4\right )\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (1+e^2\right )^2 x^2}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}+\frac {2 e^{\frac {e^{-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (3 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} x (x-4)^2+x (x-4)^2+6 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2} x^2 (x-4)+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4} \left (3 x^3-3 x^2+4\right )\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (-8-8 e^2-e^4\right ) x}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}+\frac {16 e^{\frac {e^{-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (3 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} x (x-4)^2+x (x-4)^2+6 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2} x^2 (x-4)+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4} \left (3 x^3-3 x^2+4\right )\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}}}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (3 \left (1+e^2\right )^2 x^2-2 \left (8+8 e^2+e^4\right ) x+16\right ) \exp \left (\frac {\exp \left (-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}\right ) \left (3 x (x-4)^2 \exp \left (\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}\right )+6 x^2 (x-4) \exp \left (\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2\right )+\left (3 x^3-3 x^2+4\right ) \exp \left (\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4\right )+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+x (x-4)^2\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}\right )}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {3 e^{\frac {e^{-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (3 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} x (x-4)^2+x (x-4)^2+6 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2} x^2 (x-4)+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4} \left (3 x^3-3 x^2+4\right )\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (1+e^2\right )^2 x^2}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}+\frac {2 e^{\frac {e^{-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (3 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} x (x-4)^2+x (x-4)^2+6 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2} x^2 (x-4)+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4} \left (3 x^3-3 x^2+4\right )\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (-8-8 e^2-e^4\right ) x}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}+\frac {16 e^{\frac {e^{-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (3 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} x (x-4)^2+x (x-4)^2+6 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2} x^2 (x-4)+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4} \left (3 x^3-3 x^2+4\right )\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}}}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (3 \left (1+e^2\right )^2 x^2-2 \left (8+8 e^2+e^4\right ) x+16\right ) \exp \left (\frac {\exp \left (-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}\right ) \left (3 x (x-4)^2 \exp \left (\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}\right )+6 x^2 (x-4) \exp \left (\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2\right )+\left (3 x^3-3 x^2+4\right ) \exp \left (\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4\right )+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+x (x-4)^2\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}\right )}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {3 e^{\frac {e^{-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (3 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} x (x-4)^2+x (x-4)^2+6 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2} x^2 (x-4)+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4} \left (3 x^3-3 x^2+4\right )\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (1+e^2\right )^2 x^2}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}+\frac {2 e^{\frac {e^{-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (3 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} x (x-4)^2+x (x-4)^2+6 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2} x^2 (x-4)+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4} \left (3 x^3-3 x^2+4\right )\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (-8-8 e^2-e^4\right ) x}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}+\frac {16 e^{\frac {e^{-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (3 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} x (x-4)^2+x (x-4)^2+6 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2} x^2 (x-4)+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4} \left (3 x^3-3 x^2+4\right )\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}}}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (3 \left (1+e^2\right )^2 x^2-2 \left (8+8 e^2+e^4\right ) x+16\right ) \exp \left (\frac {\exp \left (-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}\right ) \left (3 x (x-4)^2 \exp \left (\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}\right )+6 x^2 (x-4) \exp \left (\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2\right )+\left (3 x^3-3 x^2+4\right ) \exp \left (\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4\right )+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+x (x-4)^2\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}\right )}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {3 e^{\frac {e^{-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (3 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} x (x-4)^2+x (x-4)^2+6 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2} x^2 (x-4)+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4} \left (3 x^3-3 x^2+4\right )\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (1+e^2\right )^2 x^2}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}+\frac {2 e^{\frac {e^{-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (3 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} x (x-4)^2+x (x-4)^2+6 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2} x^2 (x-4)+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4} \left (3 x^3-3 x^2+4\right )\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (-8-8 e^2-e^4\right ) x}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}+\frac {16 e^{\frac {e^{-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (3 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} x (x-4)^2+x (x-4)^2+6 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2} x^2 (x-4)+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4} \left (3 x^3-3 x^2+4\right )\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}}}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (3 \left (1+e^2\right )^2 x^2-2 \left (8+8 e^2+e^4\right ) x+16\right ) \exp \left (\frac {\exp \left (-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}\right ) \left (3 x (x-4)^2 \exp \left (\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}\right )+6 x^2 (x-4) \exp \left (\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2\right )+\left (3 x^3-3 x^2+4\right ) \exp \left (\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4\right )+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+x (x-4)^2\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}\right )}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {3 e^{\frac {e^{-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (3 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} x (x-4)^2+x (x-4)^2+6 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2} x^2 (x-4)+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4} \left (3 x^3-3 x^2+4\right )\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (1+e^2\right )^2 x^2}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}+\frac {2 e^{\frac {e^{-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (3 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} x (x-4)^2+x (x-4)^2+6 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2} x^2 (x-4)+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4} \left (3 x^3-3 x^2+4\right )\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (-8-8 e^2-e^4\right ) x}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}+\frac {16 e^{\frac {e^{-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (3 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} x (x-4)^2+x (x-4)^2+6 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2} x^2 (x-4)+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4} \left (3 x^3-3 x^2+4\right )\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}}}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (3 \left (1+e^2\right )^2 x^2-2 \left (8+8 e^2+e^4\right ) x+16\right ) \exp \left (\frac {\exp \left (-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}\right ) \left (3 x (x-4)^2 \exp \left (\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}\right )+6 x^2 (x-4) \exp \left (\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2\right )+\left (3 x^3-3 x^2+4\right ) \exp \left (\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4\right )+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+x (x-4)^2\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}\right )}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {3 e^{\frac {e^{-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (3 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} x (x-4)^2+x (x-4)^2+6 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2} x^2 (x-4)+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4} \left (3 x^3-3 x^2+4\right )\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (1+e^2\right )^2 x^2}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}+\frac {2 e^{\frac {e^{-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (3 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} x (x-4)^2+x (x-4)^2+6 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2} x^2 (x-4)+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4} \left (3 x^3-3 x^2+4\right )\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (-8-8 e^2-e^4\right ) x}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}+\frac {16 e^{\frac {e^{-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (3 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} x (x-4)^2+x (x-4)^2+6 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2} x^2 (x-4)+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4} \left (3 x^3-3 x^2+4\right )\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}}}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (3 \left (1+e^2\right )^2 x^2-2 \left (8+8 e^2+e^4\right ) x+16\right ) \exp \left (\frac {\exp \left (-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}\right ) \left (3 x (x-4)^2 \exp \left (\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}\right )+6 x^2 (x-4) \exp \left (\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2\right )+\left (3 x^3-3 x^2+4\right ) \exp \left (\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4\right )+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+x (x-4)^2\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}\right )}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {3 e^{\frac {e^{-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (3 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} x (x-4)^2+x (x-4)^2+6 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2} x^2 (x-4)+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4} \left (3 x^3-3 x^2+4\right )\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (1+e^2\right )^2 x^2}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}+\frac {2 e^{\frac {e^{-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (3 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} x (x-4)^2+x (x-4)^2+6 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2} x^2 (x-4)+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4} \left (3 x^3-3 x^2+4\right )\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (-8-8 e^2-e^4\right ) x}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}+\frac {16 e^{\frac {e^{-\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} \left (3 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}} x (x-4)^2+x (x-4)^2+6 e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+2} x^2 (x-4)+2 e^2 x^2 (x-4)+e^4 \left (x^3-x^2+1\right )+e^{\frac {x \left (\left (1+e^2\right )^2 x^2-\left (8+8 e^2+e^4\right ) x+16\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}+4} \left (3 x^3-3 x^2+4\right )\right )}{\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4}}}{\left (\left (1+e^2\right )^2 x^3-\left (8+8 e^2+e^4\right ) x^2+16 x+e^4\right )^2}\right )dx\) |
Int[(E^(E^((-(((-4 + x)^2*x)/E^4) + x^2 - (2*(-4 + x)*x^2)/E^2 - x^3)/(1 + ((-4 + x)^2*x)/E^4 - x^2 + (2*(-4 + x)*x^2)/E^2 + x^3)) + (-(((-4 + x)^2* x)/E^4) + x^2 - (2*(-4 + x)*x^2)/E^2 - x^3)/(1 + ((-4 + x)^2*x)/E^4 - x^2 + (2*(-4 + x)*x^2)/E^2 + x^3))*(8*x - 14*x^2 + 3*x^3 + ((-4 + x)^2*(-4 + 3 *x))/E^4 + ((-4 + x)*(-16*x + 6*x^2))/E^2))/(-4 + x + 8*x^2 - 10*x^3 - 2*x ^4 + 9*x^5 - 6*x^6 + x^7 + ((-4 + x)^4*(-4*x^2 + x^3))/E^8 + ((-4 + x)^3*( -16*x^3 + 4*x^4))/E^6 + ((-4 + x)^2*(-8*x + 2*x^2 + 8*x^3 - 26*x^4 + 6*x^5 ))/E^4 + ((-4 + x)*(-16*x^2 + 4*x^3 + 16*x^4 - 20*x^5 + 4*x^6))/E^2),x]
3.27.92.3.1 Defintions of rubi rules used
Int[(u_.)*((v_.) + (a_.)*(Fx_) + (b_.)*(Fx_))^(p_.), x_Symbol] :> Int[u*(v + (a + b)*Fx)^p, x] /; FreeQ[{a, b}, x] && !FreeQ[Fx, x]
Int[(u_.)*(Px_)*(Qx_)^(q_), x_Symbol] :> Module[{Rx = PolyGCD[Px, Qx, x]}, Int[u*Rx^(q + 1)*PolynomialQuotient[Px, Rx, x]*PolynomialQuotient[Qx, Rx, x ]^q, x] /; NeQ[Rx, 1]] /; ILtQ[q, 0] && PolyQ[Px, x] && PolyQ[Qx, x]
Int[(u_.)*(Px_)^(p_), x_Symbol] :> With[{Qx = Factor[Px]}, Int[ExpandIntegr and[u, Qx^p, x], x] /; !SumQ[NonfreeFactors[Qx, x]]] /; PolyQ[Px, x] && Gt Q[Expon[Px, x], 2] && !BinomialQ[Px, x] && !TrinomialQ[Px, x] && ILtQ[p, 0]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(387\) vs. \(2(31)=62\).
Time = 13.21 (sec) , antiderivative size = 388, normalized size of antiderivative = 11.76
\[\frac {\left (\left ({\mathrm e}^{4}+8 \,{\mathrm e}^{2}+8\right ) {\mathrm e}^{4} {\mathrm e}^{-2} x^{2} {\mathrm e}^{{\mathrm e}^{\frac {-x \left (x -4\right )^{2} {\mathrm e}^{-4}-2 x^{2} \left (x -4\right ) {\mathrm e}^{-2}-x^{3}+x^{2}}{x \left (x -4\right )^{2} {\mathrm e}^{-4}+2 x^{2} \left (x -4\right ) {\mathrm e}^{-2}+x^{3}-x^{2}+1}}}-{\mathrm e}^{2} {\mathrm e}^{4} {\mathrm e}^{{\mathrm e}^{\frac {-x \left (x -4\right )^{2} {\mathrm e}^{-4}-2 x^{2} \left (x -4\right ) {\mathrm e}^{-2}-x^{3}+x^{2}}{x \left (x -4\right )^{2} {\mathrm e}^{-4}+2 x^{2} \left (x -4\right ) {\mathrm e}^{-2}+x^{3}-x^{2}+1}}}-16 \,{\mathrm e}^{-2} {\mathrm e}^{4} x \,{\mathrm e}^{{\mathrm e}^{\frac {-x \left (x -4\right )^{2} {\mathrm e}^{-4}-2 x^{2} \left (x -4\right ) {\mathrm e}^{-2}-x^{3}+x^{2}}{x \left (x -4\right )^{2} {\mathrm e}^{-4}+2 x^{2} \left (x -4\right ) {\mathrm e}^{-2}+x^{3}-x^{2}+1}}}-{\mathrm e}^{-2} \left ({\mathrm e}^{4}+2 \,{\mathrm e}^{2}+1\right ) {\mathrm e}^{4} x^{3} {\mathrm e}^{{\mathrm e}^{\frac {-x \left (x -4\right )^{2} {\mathrm e}^{-4}-2 x^{2} \left (x -4\right ) {\mathrm e}^{-2}-x^{3}+x^{2}}{x \left (x -4\right )^{2} {\mathrm e}^{-4}+2 x^{2} \left (x -4\right ) {\mathrm e}^{-2}+x^{3}-x^{2}+1}}}\right ) {\mathrm e}^{-2}}{x^{3} {\mathrm e}^{4}-x^{2} {\mathrm e}^{4}+2 x^{3} {\mathrm e}^{2}-8 x^{2} {\mathrm e}^{2}+x^{3}+{\mathrm e}^{4}-8 x^{2}+16 x}\]
int(((-4+3*x)*exp(ln(x-4)-2)^2+(6*x^2-16*x)*exp(ln(x-4)-2)+3*x^3-14*x^2+8* x)*exp((-x*exp(ln(x-4)-2)^2-2*x^2*exp(ln(x-4)-2)-x^3+x^2)/(x*exp(ln(x-4)-2 )^2+2*x^2*exp(ln(x-4)-2)+x^3-x^2+1))*exp(exp((-x*exp(ln(x-4)-2)^2-2*x^2*ex p(ln(x-4)-2)-x^3+x^2)/(x*exp(ln(x-4)-2)^2+2*x^2*exp(ln(x-4)-2)+x^3-x^2+1)) )/((x^3-4*x^2)*exp(ln(x-4)-2)^4+(4*x^4-16*x^3)*exp(ln(x-4)-2)^3+(6*x^5-26* x^4+8*x^3+2*x^2-8*x)*exp(ln(x-4)-2)^2+(4*x^6-20*x^5+16*x^4+4*x^3-16*x^2)*e xp(ln(x-4)-2)+x^7-6*x^6+9*x^5-2*x^4-10*x^3+8*x^2+x-4),x)
((exp(2)^2+8*exp(2)+8)/exp(-2)^2/exp(2)*x^2*exp(exp((-x*(x-4)^2*exp(-2)^2- 2*x^2*(x-4)*exp(-2)-x^3+x^2)/(x*(x-4)^2*exp(-2)^2+2*x^2*(x-4)*exp(-2)+x^3- x^2+1)))-exp(2)/exp(-2)^2*exp(exp((-x*(x-4)^2*exp(-2)^2-2*x^2*(x-4)*exp(-2 )-x^3+x^2)/(x*(x-4)^2*exp(-2)^2+2*x^2*(x-4)*exp(-2)+x^3-x^2+1)))-16/exp(2) /exp(-2)^2*x*exp(exp((-x*(x-4)^2*exp(-2)^2-2*x^2*(x-4)*exp(-2)-x^3+x^2)/(x *(x-4)^2*exp(-2)^2+2*x^2*(x-4)*exp(-2)+x^3-x^2+1)))-1/exp(2)*(exp(2)^2+2*e xp(2)+1)/exp(-2)^2*x^3*exp(exp((-x*(x-4)^2*exp(-2)^2-2*x^2*(x-4)*exp(-2)-x ^3+x^2)/(x*(x-4)^2*exp(-2)^2+2*x^2*(x-4)*exp(-2)+x^3-x^2+1))))/exp(2)/(x^3 *exp(2)^2-x^2*exp(2)^2+2*x^3*exp(2)-8*x^2*exp(2)+x^3+exp(2)^2-8*x^2+16*x)
Leaf count of result is larger than twice the leaf count of optimal. 281 vs. \(2 (30) = 60\).
Time = 0.29 (sec) , antiderivative size = 281, normalized size of antiderivative = 8.52 \[ \int \frac {e^{e^{\frac {-\frac {(-4+x)^2 x}{e^4}+x^2-\frac {2 (-4+x) x^2}{e^2}-x^3}{1+\frac {(-4+x)^2 x}{e^4}-x^2+\frac {2 (-4+x) x^2}{e^2}+x^3}}+\frac {-\frac {(-4+x)^2 x}{e^4}+x^2-\frac {2 (-4+x) x^2}{e^2}-x^3}{1+\frac {(-4+x)^2 x}{e^4}-x^2+\frac {2 (-4+x) x^2}{e^2}+x^3}} \left (8 x-14 x^2+3 x^3+\frac {(-4+x)^2 (-4+3 x)}{e^4}+\frac {(-4+x) \left (-16 x+6 x^2\right )}{e^2}\right )}{-4+x+8 x^2-10 x^3-2 x^4+9 x^5-6 x^6+x^7+\frac {(-4+x)^4 \left (-4 x^2+x^3\right )}{e^8}+\frac {(-4+x)^3 \left (-16 x^3+4 x^4\right )}{e^6}+\frac {(-4+x)^2 \left (-8 x+2 x^2+8 x^3-26 x^4+6 x^5\right )}{e^4}+\frac {(-4+x) \left (-16 x^2+4 x^3+16 x^4-20 x^5+4 x^6\right )}{e^2}} \, dx=-e^{\left (-\frac {x^{3} - 8 \, x^{2} + {\left (x^{3} - x^{2}\right )} e^{4} + 2 \, {\left (x^{3} - 4 \, x^{2}\right )} e^{2} - {\left (x^{3} - 8 \, x^{2} + {\left (x^{3} - x^{2} + 1\right )} e^{4} + 2 \, {\left (x^{3} - 4 \, x^{2}\right )} e^{2} + 16 \, x\right )} e^{\left (-\frac {x^{3} - 8 \, x^{2} + {\left (x^{3} - x^{2}\right )} e^{4} + 2 \, {\left (x^{3} - 4 \, x^{2}\right )} e^{2} + 16 \, x}{x^{3} - 8 \, x^{2} + {\left (x^{3} - x^{2} + 1\right )} e^{4} + 2 \, {\left (x^{3} - 4 \, x^{2}\right )} e^{2} + 16 \, x}\right )} + 16 \, x}{x^{3} - 8 \, x^{2} + {\left (x^{3} - x^{2} + 1\right )} e^{4} + 2 \, {\left (x^{3} - 4 \, x^{2}\right )} e^{2} + 16 \, x} + \frac {x^{3} - 8 \, x^{2} + {\left (x^{3} - x^{2}\right )} e^{4} + 2 \, {\left (x^{3} - 4 \, x^{2}\right )} e^{2} + 16 \, x}{x^{3} - 8 \, x^{2} + {\left (x^{3} - x^{2} + 1\right )} e^{4} + 2 \, {\left (x^{3} - 4 \, x^{2}\right )} e^{2} + 16 \, x}\right )} \]
integrate(((-4+3*x)*exp(log(x-4)-2)^2+(6*x^2-16*x)*exp(log(x-4)-2)+3*x^3-1 4*x^2+8*x)*exp((-x*exp(log(x-4)-2)^2-2*x^2*exp(log(x-4)-2)-x^3+x^2)/(x*exp (log(x-4)-2)^2+2*x^2*exp(log(x-4)-2)+x^3-x^2+1))*exp(exp((-x*exp(log(x-4)- 2)^2-2*x^2*exp(log(x-4)-2)-x^3+x^2)/(x*exp(log(x-4)-2)^2+2*x^2*exp(log(x-4 )-2)+x^3-x^2+1)))/((x^3-4*x^2)*exp(log(x-4)-2)^4+(4*x^4-16*x^3)*exp(log(x- 4)-2)^3+(6*x^5-26*x^4+8*x^3+2*x^2-8*x)*exp(log(x-4)-2)^2+(4*x^6-20*x^5+16* x^4+4*x^3-16*x^2)*exp(log(x-4)-2)+x^7-6*x^6+9*x^5-2*x^4-10*x^3+8*x^2+x-4), x, algorithm=\
-e^(-(x^3 - 8*x^2 + (x^3 - x^2)*e^4 + 2*(x^3 - 4*x^2)*e^2 - (x^3 - 8*x^2 + (x^3 - x^2 + 1)*e^4 + 2*(x^3 - 4*x^2)*e^2 + 16*x)*e^(-(x^3 - 8*x^2 + (x^3 - x^2)*e^4 + 2*(x^3 - 4*x^2)*e^2 + 16*x)/(x^3 - 8*x^2 + (x^3 - x^2 + 1)*e ^4 + 2*(x^3 - 4*x^2)*e^2 + 16*x)) + 16*x)/(x^3 - 8*x^2 + (x^3 - x^2 + 1)*e ^4 + 2*(x^3 - 4*x^2)*e^2 + 16*x) + (x^3 - 8*x^2 + (x^3 - x^2)*e^4 + 2*(x^3 - 4*x^2)*e^2 + 16*x)/(x^3 - 8*x^2 + (x^3 - x^2 + 1)*e^4 + 2*(x^3 - 4*x^2) *e^2 + 16*x))
Leaf count of result is larger than twice the leaf count of optimal. 63 vs. \(2 (20) = 40\).
Time = 4.52 (sec) , antiderivative size = 63, normalized size of antiderivative = 1.91 \[ \int \frac {e^{e^{\frac {-\frac {(-4+x)^2 x}{e^4}+x^2-\frac {2 (-4+x) x^2}{e^2}-x^3}{1+\frac {(-4+x)^2 x}{e^4}-x^2+\frac {2 (-4+x) x^2}{e^2}+x^3}}+\frac {-\frac {(-4+x)^2 x}{e^4}+x^2-\frac {2 (-4+x) x^2}{e^2}-x^3}{1+\frac {(-4+x)^2 x}{e^4}-x^2+\frac {2 (-4+x) x^2}{e^2}+x^3}} \left (8 x-14 x^2+3 x^3+\frac {(-4+x)^2 (-4+3 x)}{e^4}+\frac {(-4+x) \left (-16 x+6 x^2\right )}{e^2}\right )}{-4+x+8 x^2-10 x^3-2 x^4+9 x^5-6 x^6+x^7+\frac {(-4+x)^4 \left (-4 x^2+x^3\right )}{e^8}+\frac {(-4+x)^3 \left (-16 x^3+4 x^4\right )}{e^6}+\frac {(-4+x)^2 \left (-8 x+2 x^2+8 x^3-26 x^4+6 x^5\right )}{e^4}+\frac {(-4+x) \left (-16 x^2+4 x^3+16 x^4-20 x^5+4 x^6\right )}{e^2}} \, dx=- e^{e^{\frac {- x^{3} - \frac {2 x^{2} \left (x - 4\right )}{e^{2}} + x^{2} - \frac {x \left (x - 4\right )^{2}}{e^{4}}}{x^{3} + \frac {2 x^{2} \left (x - 4\right )}{e^{2}} - x^{2} + \frac {x \left (x - 4\right )^{2}}{e^{4}} + 1}}} \]
integrate(((-4+3*x)*exp(ln(x-4)-2)**2+(6*x**2-16*x)*exp(ln(x-4)-2)+3*x**3- 14*x**2+8*x)*exp((-x*exp(ln(x-4)-2)**2-2*x**2*exp(ln(x-4)-2)-x**3+x**2)/(x *exp(ln(x-4)-2)**2+2*x**2*exp(ln(x-4)-2)+x**3-x**2+1))*exp(exp((-x*exp(ln( x-4)-2)**2-2*x**2*exp(ln(x-4)-2)-x**3+x**2)/(x*exp(ln(x-4)-2)**2+2*x**2*ex p(ln(x-4)-2)+x**3-x**2+1)))/((x**3-4*x**2)*exp(ln(x-4)-2)**4+(4*x**4-16*x* *3)*exp(ln(x-4)-2)**3+(6*x**5-26*x**4+8*x**3+2*x**2-8*x)*exp(ln(x-4)-2)**2 +(4*x**6-20*x**5+16*x**4+4*x**3-16*x**2)*exp(ln(x-4)-2)+x**7-6*x**6+9*x**5 -2*x**4-10*x**3+8*x**2+x-4),x)
-exp(exp((-x**3 - 2*x**2*(x - 4)*exp(-2) + x**2 - x*(x - 4)**2*exp(-4))/(x **3 + 2*x**2*(x - 4)*exp(-2) - x**2 + x*(x - 4)**2*exp(-4) + 1)))
Leaf count of result is larger than twice the leaf count of optimal. 947 vs. \(2 (30) = 60\).
Time = 5.23 (sec) , antiderivative size = 947, normalized size of antiderivative = 28.70 \[ \int \frac {e^{e^{\frac {-\frac {(-4+x)^2 x}{e^4}+x^2-\frac {2 (-4+x) x^2}{e^2}-x^3}{1+\frac {(-4+x)^2 x}{e^4}-x^2+\frac {2 (-4+x) x^2}{e^2}+x^3}}+\frac {-\frac {(-4+x)^2 x}{e^4}+x^2-\frac {2 (-4+x) x^2}{e^2}-x^3}{1+\frac {(-4+x)^2 x}{e^4}-x^2+\frac {2 (-4+x) x^2}{e^2}+x^3}} \left (8 x-14 x^2+3 x^3+\frac {(-4+x)^2 (-4+3 x)}{e^4}+\frac {(-4+x) \left (-16 x+6 x^2\right )}{e^2}\right )}{-4+x+8 x^2-10 x^3-2 x^4+9 x^5-6 x^6+x^7+\frac {(-4+x)^4 \left (-4 x^2+x^3\right )}{e^8}+\frac {(-4+x)^3 \left (-16 x^3+4 x^4\right )}{e^6}+\frac {(-4+x)^2 \left (-8 x+2 x^2+8 x^3-26 x^4+6 x^5\right )}{e^4}+\frac {(-4+x) \left (-16 x^2+4 x^3+16 x^4-20 x^5+4 x^6\right )}{e^2}} \, dx=\text {Too large to display} \]
integrate(((-4+3*x)*exp(log(x-4)-2)^2+(6*x^2-16*x)*exp(log(x-4)-2)+3*x^3-1 4*x^2+8*x)*exp((-x*exp(log(x-4)-2)^2-2*x^2*exp(log(x-4)-2)-x^3+x^2)/(x*exp (log(x-4)-2)^2+2*x^2*exp(log(x-4)-2)+x^3-x^2+1))*exp(exp((-x*exp(log(x-4)- 2)^2-2*x^2*exp(log(x-4)-2)-x^3+x^2)/(x*exp(log(x-4)-2)^2+2*x^2*exp(log(x-4 )-2)+x^3-x^2+1)))/((x^3-4*x^2)*exp(log(x-4)-2)^4+(4*x^4-16*x^3)*exp(log(x- 4)-2)^3+(6*x^5-26*x^4+8*x^3+2*x^2-8*x)*exp(log(x-4)-2)^2+(4*x^6-20*x^5+16* x^4+4*x^3-16*x^2)*exp(log(x-4)-2)+x^7-6*x^6+9*x^5-2*x^4-10*x^3+8*x^2+x-4), x, algorithm=\
-e^(e^(-x^2*e^8/(x^3*(e^8 + 4*e^6 + 6*e^4 + 4*e^2 + 1) - x^2*(e^8 + 10*e^6 + 25*e^4 + 24*e^2 + 8) + 16*x*(e^4 + 2*e^2 + 1) + e^8 + 2*e^6 + e^4) - 10 *x^2*e^6/(x^3*(e^8 + 4*e^6 + 6*e^4 + 4*e^2 + 1) - x^2*(e^8 + 10*e^6 + 25*e ^4 + 24*e^2 + 8) + 16*x*(e^4 + 2*e^2 + 1) + e^8 + 2*e^6 + e^4) - 25*x^2*e^ 4/(x^3*(e^8 + 4*e^6 + 6*e^4 + 4*e^2 + 1) - x^2*(e^8 + 10*e^6 + 25*e^4 + 24 *e^2 + 8) + 16*x*(e^4 + 2*e^2 + 1) + e^8 + 2*e^6 + e^4) + x^2*e^4/(x^3*(e^ 4 + 2*e^2 + 1) - x^2*(e^4 + 8*e^2 + 8) + 16*x + e^4) - 24*x^2*e^2/(x^3*(e^ 8 + 4*e^6 + 6*e^4 + 4*e^2 + 1) - x^2*(e^8 + 10*e^6 + 25*e^4 + 24*e^2 + 8) + 16*x*(e^4 + 2*e^2 + 1) + e^8 + 2*e^6 + e^4) + 8*x^2*e^2/(x^3*(e^4 + 2*e^ 2 + 1) - x^2*(e^4 + 8*e^2 + 8) + 16*x + e^4) - 8*x^2/(x^3*(e^8 + 4*e^6 + 6 *e^4 + 4*e^2 + 1) - x^2*(e^8 + 10*e^6 + 25*e^4 + 24*e^2 + 8) + 16*x*(e^4 + 2*e^2 + 1) + e^8 + 2*e^6 + e^4) + 8*x^2/(x^3*(e^4 + 2*e^2 + 1) - x^2*(e^4 + 8*e^2 + 8) + 16*x + e^4) + 16*x*e^4/(x^3*(e^8 + 4*e^6 + 6*e^4 + 4*e^2 + 1) - x^2*(e^8 + 10*e^6 + 25*e^4 + 24*e^2 + 8) + 16*x*(e^4 + 2*e^2 + 1) + e^8 + 2*e^6 + e^4) + 32*x*e^2/(x^3*(e^8 + 4*e^6 + 6*e^4 + 4*e^2 + 1) - x^2 *(e^8 + 10*e^6 + 25*e^4 + 24*e^2 + 8) + 16*x*(e^4 + 2*e^2 + 1) + e^8 + 2*e ^6 + e^4) + 16*x/(x^3*(e^8 + 4*e^6 + 6*e^4 + 4*e^2 + 1) - x^2*(e^8 + 10*e^ 6 + 25*e^4 + 24*e^2 + 8) + 16*x*(e^4 + 2*e^2 + 1) + e^8 + 2*e^6 + e^4) - 1 6*x/(x^3*(e^4 + 2*e^2 + 1) - x^2*(e^4 + 8*e^2 + 8) + 16*x + e^4) + e^8/(x^ 3*(e^8 + 4*e^6 + 6*e^4 + 4*e^2 + 1) - x^2*(e^8 + 10*e^6 + 25*e^4 + 24*e...
\[ \int \frac {e^{e^{\frac {-\frac {(-4+x)^2 x}{e^4}+x^2-\frac {2 (-4+x) x^2}{e^2}-x^3}{1+\frac {(-4+x)^2 x}{e^4}-x^2+\frac {2 (-4+x) x^2}{e^2}+x^3}}+\frac {-\frac {(-4+x)^2 x}{e^4}+x^2-\frac {2 (-4+x) x^2}{e^2}-x^3}{1+\frac {(-4+x)^2 x}{e^4}-x^2+\frac {2 (-4+x) x^2}{e^2}+x^3}} \left (8 x-14 x^2+3 x^3+\frac {(-4+x)^2 (-4+3 x)}{e^4}+\frac {(-4+x) \left (-16 x+6 x^2\right )}{e^2}\right )}{-4+x+8 x^2-10 x^3-2 x^4+9 x^5-6 x^6+x^7+\frac {(-4+x)^4 \left (-4 x^2+x^3\right )}{e^8}+\frac {(-4+x)^3 \left (-16 x^3+4 x^4\right )}{e^6}+\frac {(-4+x)^2 \left (-8 x+2 x^2+8 x^3-26 x^4+6 x^5\right )}{e^4}+\frac {(-4+x) \left (-16 x^2+4 x^3+16 x^4-20 x^5+4 x^6\right )}{e^2}} \, dx=\int { \frac {{\left (3 \, x^{3} - 14 \, x^{2} + {\left (3 \, x - 4\right )} e^{\left (2 \, \log \left (x - 4\right ) - 4\right )} + 2 \, {\left (3 \, x^{2} - 8 \, x\right )} e^{\left (\log \left (x - 4\right ) - 2\right )} + 8 \, x\right )} e^{\left (-\frac {x^{3} + 2 \, x^{2} e^{\left (\log \left (x - 4\right ) - 2\right )} - x^{2} + x e^{\left (2 \, \log \left (x - 4\right ) - 4\right )}}{x^{3} + 2 \, x^{2} e^{\left (\log \left (x - 4\right ) - 2\right )} - x^{2} + x e^{\left (2 \, \log \left (x - 4\right ) - 4\right )} + 1} + e^{\left (-\frac {x^{3} + 2 \, x^{2} e^{\left (\log \left (x - 4\right ) - 2\right )} - x^{2} + x e^{\left (2 \, \log \left (x - 4\right ) - 4\right )}}{x^{3} + 2 \, x^{2} e^{\left (\log \left (x - 4\right ) - 2\right )} - x^{2} + x e^{\left (2 \, \log \left (x - 4\right ) - 4\right )} + 1}\right )}\right )}}{x^{7} - 6 \, x^{6} + 9 \, x^{5} - 2 \, x^{4} - 10 \, x^{3} + 8 \, x^{2} + {\left (x^{3} - 4 \, x^{2}\right )} e^{\left (4 \, \log \left (x - 4\right ) - 8\right )} + 4 \, {\left (x^{4} - 4 \, x^{3}\right )} e^{\left (3 \, \log \left (x - 4\right ) - 6\right )} + 2 \, {\left (3 \, x^{5} - 13 \, x^{4} + 4 \, x^{3} + x^{2} - 4 \, x\right )} e^{\left (2 \, \log \left (x - 4\right ) - 4\right )} + 4 \, {\left (x^{6} - 5 \, x^{5} + 4 \, x^{4} + x^{3} - 4 \, x^{2}\right )} e^{\left (\log \left (x - 4\right ) - 2\right )} + x - 4} \,d x } \]
integrate(((-4+3*x)*exp(log(x-4)-2)^2+(6*x^2-16*x)*exp(log(x-4)-2)+3*x^3-1 4*x^2+8*x)*exp((-x*exp(log(x-4)-2)^2-2*x^2*exp(log(x-4)-2)-x^3+x^2)/(x*exp (log(x-4)-2)^2+2*x^2*exp(log(x-4)-2)+x^3-x^2+1))*exp(exp((-x*exp(log(x-4)- 2)^2-2*x^2*exp(log(x-4)-2)-x^3+x^2)/(x*exp(log(x-4)-2)^2+2*x^2*exp(log(x-4 )-2)+x^3-x^2+1)))/((x^3-4*x^2)*exp(log(x-4)-2)^4+(4*x^4-16*x^3)*exp(log(x- 4)-2)^3+(6*x^5-26*x^4+8*x^3+2*x^2-8*x)*exp(log(x-4)-2)^2+(4*x^6-20*x^5+16* x^4+4*x^3-16*x^2)*exp(log(x-4)-2)+x^7-6*x^6+9*x^5-2*x^4-10*x^3+8*x^2+x-4), x, algorithm=\
integrate((3*x^3 - 14*x^2 + (3*x - 4)*e^(2*log(x - 4) - 4) + 2*(3*x^2 - 8* x)*e^(log(x - 4) - 2) + 8*x)*e^(-(x^3 + 2*x^2*e^(log(x - 4) - 2) - x^2 + x *e^(2*log(x - 4) - 4))/(x^3 + 2*x^2*e^(log(x - 4) - 2) - x^2 + x*e^(2*log( x - 4) - 4) + 1) + e^(-(x^3 + 2*x^2*e^(log(x - 4) - 2) - x^2 + x*e^(2*log( x - 4) - 4))/(x^3 + 2*x^2*e^(log(x - 4) - 2) - x^2 + x*e^(2*log(x - 4) - 4 ) + 1)))/(x^7 - 6*x^6 + 9*x^5 - 2*x^4 - 10*x^3 + 8*x^2 + (x^3 - 4*x^2)*e^( 4*log(x - 4) - 8) + 4*(x^4 - 4*x^3)*e^(3*log(x - 4) - 6) + 2*(3*x^5 - 13*x ^4 + 4*x^3 + x^2 - 4*x)*e^(2*log(x - 4) - 4) + 4*(x^6 - 5*x^5 + 4*x^4 + x^ 3 - 4*x^2)*e^(log(x - 4) - 2) + x - 4), x)
Time = 14.58 (sec) , antiderivative size = 361, normalized size of antiderivative = 10.94 \[ \int \frac {e^{e^{\frac {-\frac {(-4+x)^2 x}{e^4}+x^2-\frac {2 (-4+x) x^2}{e^2}-x^3}{1+\frac {(-4+x)^2 x}{e^4}-x^2+\frac {2 (-4+x) x^2}{e^2}+x^3}}+\frac {-\frac {(-4+x)^2 x}{e^4}+x^2-\frac {2 (-4+x) x^2}{e^2}-x^3}{1+\frac {(-4+x)^2 x}{e^4}-x^2+\frac {2 (-4+x) x^2}{e^2}+x^3}} \left (8 x-14 x^2+3 x^3+\frac {(-4+x)^2 (-4+3 x)}{e^4}+\frac {(-4+x) \left (-16 x+6 x^2\right )}{e^2}\right )}{-4+x+8 x^2-10 x^3-2 x^4+9 x^5-6 x^6+x^7+\frac {(-4+x)^4 \left (-4 x^2+x^3\right )}{e^8}+\frac {(-4+x)^3 \left (-16 x^3+4 x^4\right )}{e^6}+\frac {(-4+x)^2 \left (-8 x+2 x^2+8 x^3-26 x^4+6 x^5\right )}{e^4}+\frac {(-4+x) \left (-16 x^2+4 x^3+16 x^4-20 x^5+4 x^6\right )}{e^2}} \, dx=-{\mathrm {e}}^{{\mathrm {e}}^{\frac {x^2}{16\,x\,{\mathrm {e}}^{-4}-8\,x^2\,{\mathrm {e}}^{-2}+2\,x^3\,{\mathrm {e}}^{-2}-8\,x^2\,{\mathrm {e}}^{-4}+x^3\,{\mathrm {e}}^{-4}-x^2+x^3+1}}\,{\mathrm {e}}^{-\frac {x^3}{16\,x\,{\mathrm {e}}^{-4}-8\,x^2\,{\mathrm {e}}^{-2}+2\,x^3\,{\mathrm {e}}^{-2}-8\,x^2\,{\mathrm {e}}^{-4}+x^3\,{\mathrm {e}}^{-4}-x^2+x^3+1}}\,{\mathrm {e}}^{-\frac {16\,x\,{\mathrm {e}}^{-4}}{16\,x\,{\mathrm {e}}^{-4}-8\,x^2\,{\mathrm {e}}^{-2}+2\,x^3\,{\mathrm {e}}^{-2}-8\,x^2\,{\mathrm {e}}^{-4}+x^3\,{\mathrm {e}}^{-4}-x^2+x^3+1}}\,{\mathrm {e}}^{-\frac {2\,x^3\,{\mathrm {e}}^{-2}}{16\,x\,{\mathrm {e}}^{-4}-8\,x^2\,{\mathrm {e}}^{-2}+2\,x^3\,{\mathrm {e}}^{-2}-8\,x^2\,{\mathrm {e}}^{-4}+x^3\,{\mathrm {e}}^{-4}-x^2+x^3+1}}\,{\mathrm {e}}^{-\frac {x^3\,{\mathrm {e}}^{-4}}{16\,x\,{\mathrm {e}}^{-4}-8\,x^2\,{\mathrm {e}}^{-2}+2\,x^3\,{\mathrm {e}}^{-2}-8\,x^2\,{\mathrm {e}}^{-4}+x^3\,{\mathrm {e}}^{-4}-x^2+x^3+1}}\,{\mathrm {e}}^{\frac {8\,x^2\,{\mathrm {e}}^{-2}}{16\,x\,{\mathrm {e}}^{-4}-8\,x^2\,{\mathrm {e}}^{-2}+2\,x^3\,{\mathrm {e}}^{-2}-8\,x^2\,{\mathrm {e}}^{-4}+x^3\,{\mathrm {e}}^{-4}-x^2+x^3+1}}\,{\mathrm {e}}^{\frac {8\,x^2\,{\mathrm {e}}^{-4}}{16\,x\,{\mathrm {e}}^{-4}-8\,x^2\,{\mathrm {e}}^{-2}+2\,x^3\,{\mathrm {e}}^{-2}-8\,x^2\,{\mathrm {e}}^{-4}+x^3\,{\mathrm {e}}^{-4}-x^2+x^3+1}}} \]
int((exp(exp(-(x*exp(2*log(x - 4) - 4) + 2*x^2*exp(log(x - 4) - 2) - x^2 + x^3)/(x*exp(2*log(x - 4) - 4) + 2*x^2*exp(log(x - 4) - 2) - x^2 + x^3 + 1 )))*exp(-(x*exp(2*log(x - 4) - 4) + 2*x^2*exp(log(x - 4) - 2) - x^2 + x^3) /(x*exp(2*log(x - 4) - 4) + 2*x^2*exp(log(x - 4) - 2) - x^2 + x^3 + 1))*(8 *x - exp(log(x - 4) - 2)*(16*x - 6*x^2) - 14*x^2 + 3*x^3 + exp(2*log(x - 4 ) - 4)*(3*x - 4)))/(x - exp(4*log(x - 4) - 8)*(4*x^2 - x^3) - exp(3*log(x - 4) - 6)*(16*x^3 - 4*x^4) + 8*x^2 - 10*x^3 - 2*x^4 + 9*x^5 - 6*x^6 + x^7 + exp(2*log(x - 4) - 4)*(2*x^2 - 8*x + 8*x^3 - 26*x^4 + 6*x^5) + exp(log(x - 4) - 2)*(4*x^3 - 16*x^2 + 16*x^4 - 20*x^5 + 4*x^6) - 4),x)
-exp(exp(x^2/(16*x*exp(-4) - 8*x^2*exp(-2) + 2*x^3*exp(-2) - 8*x^2*exp(-4) + x^3*exp(-4) - x^2 + x^3 + 1))*exp(-x^3/(16*x*exp(-4) - 8*x^2*exp(-2) + 2*x^3*exp(-2) - 8*x^2*exp(-4) + x^3*exp(-4) - x^2 + x^3 + 1))*exp(-(16*x*e xp(-4))/(16*x*exp(-4) - 8*x^2*exp(-2) + 2*x^3*exp(-2) - 8*x^2*exp(-4) + x^ 3*exp(-4) - x^2 + x^3 + 1))*exp(-(2*x^3*exp(-2))/(16*x*exp(-4) - 8*x^2*exp (-2) + 2*x^3*exp(-2) - 8*x^2*exp(-4) + x^3*exp(-4) - x^2 + x^3 + 1))*exp(- (x^3*exp(-4))/(16*x*exp(-4) - 8*x^2*exp(-2) + 2*x^3*exp(-2) - 8*x^2*exp(-4 ) + x^3*exp(-4) - x^2 + x^3 + 1))*exp((8*x^2*exp(-2))/(16*x*exp(-4) - 8*x^ 2*exp(-2) + 2*x^3*exp(-2) - 8*x^2*exp(-4) + x^3*exp(-4) - x^2 + x^3 + 1))* exp((8*x^2*exp(-4))/(16*x*exp(-4) - 8*x^2*exp(-2) + 2*x^3*exp(-2) - 8*x^2* exp(-4) + x^3*exp(-4) - x^2 + x^3 + 1)))