Integrand size = 225, antiderivative size = 33 \[ \int \frac {e^{\frac {-20+4 e^4+e^{e^x} \left (4-e^x\right )+3 x-4 x^2+e^x \left (5-e^4-x+x^2\right )}{-5+e^4+e^{e^x}+x-x^2}} \left (5-e^4-e^{2 e^x+x}-x^2+e^x \left (-25-e^8+10 x-11 x^2+2 x^3-x^4+e^4 \left (10-2 x+2 x^2\right )\right )+e^{e^x} \left (-1+e^x \left (10-2 e^4-x+2 x^2\right )\right )\right )}{25+e^8+e^{2 e^x}-10 x+11 x^2-2 x^3+x^4+e^4 \left (-10+2 x-2 x^2\right )+e^{e^x} \left (-10+2 e^4+2 x-2 x^2\right )} \, dx=e^{4-e^x+\frac {x}{5-e^4-e^{e^x}-x+x^2}} \]
Time = 0.46 (sec) , antiderivative size = 30, normalized size of antiderivative = 0.91 \[ \int \frac {e^{\frac {-20+4 e^4+e^{e^x} \left (4-e^x\right )+3 x-4 x^2+e^x \left (5-e^4-x+x^2\right )}{-5+e^4+e^{e^x}+x-x^2}} \left (5-e^4-e^{2 e^x+x}-x^2+e^x \left (-25-e^8+10 x-11 x^2+2 x^3-x^4+e^4 \left (10-2 x+2 x^2\right )\right )+e^{e^x} \left (-1+e^x \left (10-2 e^4-x+2 x^2\right )\right )\right )}{25+e^8+e^{2 e^x}-10 x+11 x^2-2 x^3+x^4+e^4 \left (-10+2 x-2 x^2\right )+e^{e^x} \left (-10+2 e^4+2 x-2 x^2\right )} \, dx=e^{4-e^x-\frac {x}{-5+e^4+e^{e^x}+x-x^2}} \]
Integrate[(E^((-20 + 4*E^4 + E^E^x*(4 - E^x) + 3*x - 4*x^2 + E^x*(5 - E^4 - x + x^2))/(-5 + E^4 + E^E^x + x - x^2))*(5 - E^4 - E^(2*E^x + x) - x^2 + E^x*(-25 - E^8 + 10*x - 11*x^2 + 2*x^3 - x^4 + E^4*(10 - 2*x + 2*x^2)) + E^E^x*(-1 + E^x*(10 - 2*E^4 - x + 2*x^2))))/(25 + E^8 + E^(2*E^x) - 10*x + 11*x^2 - 2*x^3 + x^4 + E^4*(-10 + 2*x - 2*x^2) + E^E^x*(-10 + 2*E^4 + 2*x - 2*x^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.
| \(\displaystyle \int \frac {\left (-x^2+e^{e^x} \left (e^x \left (2 x^2-x-2 e^4+10\right )-1\right )+e^x \left (-x^4+2 x^3-11 x^2+e^4 \left (2 x^2-2 x+10\right )+10 x-e^8-25\right )-e^{x+2 e^x}-e^4+5\right ) \exp \left (\frac {-4 x^2+e^x \left (x^2-x-e^4+5\right )+3 x+e^{e^x} \left (4-e^x\right )+4 e^4-20}{-x^2+x+e^{e^x}+e^4-5}\right )}{x^4-2 x^3+11 x^2+e^4 \left (-2 x^2+2 x-10\right )+e^{e^x} \left (-2 x^2+2 x+2 e^4-10\right )-10 x+e^{2 e^x}+e^8+25} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {\left (-x^2+e^{e^x} \left (e^x \left (2 x^2-x-2 e^4+10\right )-1\right )+e^x \left (-x^4+2 x^3-11 x^2+e^4 \left (2 x^2-2 x+10\right )+10 x-e^8-25\right )-e^{x+2 e^x}+5 \left (1-\frac {e^4}{5}\right )\right ) \exp \left (\frac {-4 x^2+e^x \left (x^2-x-e^4+5\right )+3 x+e^{e^x} \left (4-e^x\right )-20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {x^2 \exp \left (\frac {-4 x^2+e^x \left (x^2-x-e^4+5\right )+3 x+e^{e^x} \left (4-e^x\right )-20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}-\frac {\exp \left (\frac {-4 x^2+e^x \left (x^2-x-e^4+5\right )+3 x+e^{e^x} \left (4-e^x\right )-20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}+e^x\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}+\frac {\left (5-e^4\right ) \exp \left (\frac {-4 x^2+e^x \left (x^2-x-e^4+5\right )+3 x+e^{e^x} \left (4-e^x\right )-20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}+\frac {\left (-x^4+2 x^3+2 e^{e^x} x^2-11 \left (1-\frac {2 e^4}{11}\right ) x^2-e^{e^x} x+10 \left (1-\frac {e^4}{5}\right ) x-e^{2 e^x}+10 \left (1-\frac {e^4}{5}\right ) e^{e^x}-25 \left (1+\frac {1}{25} e^4 \left (e^4-10\right )\right )\right ) \exp \left (\frac {-4 x^2+e^x \left (x^2-x-e^4+5\right )+3 x+e^{e^x} \left (4-e^x\right )-20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}+x\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (-x^2-e^x \left (x^2-x+5\right )^2+2 e^{x+4} \left (x^2-x+5\right )+e^{x+e^x} \left (2 x^2-x+10\right )-e^{e^x}-e^{x+8}-2 e^{x+e^x+4}-e^{x+2 e^x}+5 \left (1-\frac {e^4}{5}\right )\right ) \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {x^2 \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}-\frac {\exp \left (e^x-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}+\frac {\left (5-e^4\right ) \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}+\frac {\left (-x^4+2 x^3+2 e^{e^x} x^2-11 \left (1-\frac {2 e^4}{11}\right ) x^2-e^{e^x} x+10 \left (1-\frac {e^4}{5}\right ) x-e^{2 e^x}+10 \left (1-\frac {e^4}{5}\right ) e^{e^x}-25 \left (1+\frac {1}{25} e^4 \left (e^4-10\right )\right )\right ) \exp \left (x-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (-x^2-e^x \left (x^2-x+5\right )^2+2 e^{x+4} \left (x^2-x+5\right )+e^{x+e^x} \left (2 x^2-x+10\right )-e^{e^x}-e^{x+8}-2 e^{x+e^x+4}-e^{x+2 e^x}+5 \left (1-\frac {e^4}{5}\right )\right ) \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {x^2 \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}-\frac {\exp \left (e^x-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}+\frac {\left (5-e^4\right ) \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}+\frac {\left (-x^4+2 x^3+2 e^{e^x} x^2-11 \left (1-\frac {2 e^4}{11}\right ) x^2-e^{e^x} x+10 \left (1-\frac {e^4}{5}\right ) x-e^{2 e^x}+10 \left (1-\frac {e^4}{5}\right ) e^{e^x}-25 \left (1+\frac {1}{25} e^4 \left (e^4-10\right )\right )\right ) \exp \left (x-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (-x^2-e^x \left (x^2-x+5\right )^2+2 e^{x+4} \left (x^2-x+5\right )+e^{x+e^x} \left (2 x^2-x+10\right )-e^{e^x}-e^{x+8}-2 e^{x+e^x+4}-e^{x+2 e^x}+5 \left (1-\frac {e^4}{5}\right )\right ) \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {x^2 \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}-\frac {\exp \left (e^x-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}+\frac {\left (5-e^4\right ) \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}+\frac {\left (-x^4+2 x^3+2 e^{e^x} x^2-11 \left (1-\frac {2 e^4}{11}\right ) x^2-e^{e^x} x+10 \left (1-\frac {e^4}{5}\right ) x-e^{2 e^x}+10 \left (1-\frac {e^4}{5}\right ) e^{e^x}-25 \left (1+\frac {1}{25} e^4 \left (e^4-10\right )\right )\right ) \exp \left (x-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (-x^2-e^x \left (x^2-x+5\right )^2+2 e^{x+4} \left (x^2-x+5\right )+e^{x+e^x} \left (2 x^2-x+10\right )-e^{e^x}-e^{x+8}-2 e^{x+e^x+4}-e^{x+2 e^x}+5 \left (1-\frac {e^4}{5}\right )\right ) \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {x^2 \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}-\frac {\exp \left (e^x-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}+\frac {\left (5-e^4\right ) \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}+\frac {\left (-x^4+2 x^3+2 e^{e^x} x^2-11 \left (1-\frac {2 e^4}{11}\right ) x^2-e^{e^x} x+10 \left (1-\frac {e^4}{5}\right ) x-e^{2 e^x}+10 \left (1-\frac {e^4}{5}\right ) e^{e^x}-25 \left (1+\frac {1}{25} e^4 \left (e^4-10\right )\right )\right ) \exp \left (x-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (-x^2-e^x \left (x^2-x+5\right )^2+2 e^{x+4} \left (x^2-x+5\right )+e^{x+e^x} \left (2 x^2-x+10\right )-e^{e^x}-e^{x+8}-2 e^{x+e^x+4}-e^{x+2 e^x}+5 \left (1-\frac {e^4}{5}\right )\right ) \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {x^2 \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}-\frac {\exp \left (e^x-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}+\frac {\left (5-e^4\right ) \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}+\frac {\left (-x^4+2 x^3+2 e^{e^x} x^2-11 \left (1-\frac {2 e^4}{11}\right ) x^2-e^{e^x} x+10 \left (1-\frac {e^4}{5}\right ) x-e^{2 e^x}+10 \left (1-\frac {e^4}{5}\right ) e^{e^x}-25 \left (1+\frac {1}{25} e^4 \left (e^4-10\right )\right )\right ) \exp \left (x-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (-x^2-e^x \left (x^2-x+5\right )^2+2 e^{x+4} \left (x^2-x+5\right )+e^{x+e^x} \left (2 x^2-x+10\right )-e^{e^x}-e^{x+8}-2 e^{x+e^x+4}-e^{x+2 e^x}+5 \left (1-\frac {e^4}{5}\right )\right ) \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {x^2 \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}-\frac {\exp \left (e^x-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}+\frac {\left (5-e^4\right ) \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}+\frac {\left (-x^4+2 x^3+2 e^{e^x} x^2-11 \left (1-\frac {2 e^4}{11}\right ) x^2-e^{e^x} x+10 \left (1-\frac {e^4}{5}\right ) x-e^{2 e^x}+10 \left (1-\frac {e^4}{5}\right ) e^{e^x}-25 \left (1+\frac {1}{25} e^4 \left (e^4-10\right )\right )\right ) \exp \left (x-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (-x^2-e^x \left (x^2-x+5\right )^2+2 e^{x+4} \left (x^2-x+5\right )+e^{x+e^x} \left (2 x^2-x+10\right )-e^{e^x}-e^{x+8}-2 e^{x+e^x+4}-e^{x+2 e^x}+5 \left (1-\frac {e^4}{5}\right )\right ) \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {x^2 \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}-\frac {\exp \left (e^x-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}+\frac {\left (5-e^4\right ) \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}+\frac {\left (-x^4+2 x^3+2 e^{e^x} x^2-11 \left (1-\frac {2 e^4}{11}\right ) x^2-e^{e^x} x+10 \left (1-\frac {e^4}{5}\right ) x-e^{2 e^x}+10 \left (1-\frac {e^4}{5}\right ) e^{e^x}-25 \left (1+\frac {1}{25} e^4 \left (e^4-10\right )\right )\right ) \exp \left (x-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (-x^2-e^x \left (x^2-x+5\right )^2+2 e^{x+4} \left (x^2-x+5\right )+e^{x+e^x} \left (2 x^2-x+10\right )-e^{e^x}-e^{x+8}-2 e^{x+e^x+4}-e^{x+2 e^x}+5 \left (1-\frac {e^4}{5}\right )\right ) \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {x^2 \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}-\frac {\exp \left (e^x-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}+\frac {\left (5-e^4\right ) \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}+\frac {\left (-x^4+2 x^3+2 e^{e^x} x^2-11 \left (1-\frac {2 e^4}{11}\right ) x^2-e^{e^x} x+10 \left (1-\frac {e^4}{5}\right ) x-e^{2 e^x}+10 \left (1-\frac {e^4}{5}\right ) e^{e^x}-25 \left (1+\frac {1}{25} e^4 \left (e^4-10\right )\right )\right ) \exp \left (x-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (-x^2-e^x \left (x^2-x+5\right )^2+2 e^{x+4} \left (x^2-x+5\right )+e^{x+e^x} \left (2 x^2-x+10\right )-e^{e^x}-e^{x+8}-2 e^{x+e^x+4}-e^{x+2 e^x}+5 \left (1-\frac {e^4}{5}\right )\right ) \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {x^2 \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}-\frac {\exp \left (e^x-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}+\frac {\left (5-e^4\right ) \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}+\frac {\left (-x^4+2 x^3+2 e^{e^x} x^2-11 \left (1-\frac {2 e^4}{11}\right ) x^2-e^{e^x} x+10 \left (1-\frac {e^4}{5}\right ) x-e^{2 e^x}+10 \left (1-\frac {e^4}{5}\right ) e^{e^x}-25 \left (1+\frac {1}{25} e^4 \left (e^4-10\right )\right )\right ) \exp \left (x-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (-x^2-e^x \left (x^2-x+5\right )^2+2 e^{x+4} \left (x^2-x+5\right )+e^{x+e^x} \left (2 x^2-x+10\right )-e^{e^x}-e^{x+8}-2 e^{x+e^x+4}-e^{x+2 e^x}+5 \left (1-\frac {e^4}{5}\right )\right ) \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {x^2 \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}-\frac {\exp \left (e^x-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}+\frac {\left (5-e^4\right ) \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}+\frac {\left (-x^4+2 x^3+2 e^{e^x} x^2-11 \left (1-\frac {2 e^4}{11}\right ) x^2-e^{e^x} x+10 \left (1-\frac {e^4}{5}\right ) x-e^{2 e^x}+10 \left (1-\frac {e^4}{5}\right ) e^{e^x}-25 \left (1+\frac {1}{25} e^4 \left (e^4-10\right )\right )\right ) \exp \left (x-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (-x^2-e^x \left (x^2-x+5\right )^2+2 e^{x+4} \left (x^2-x+5\right )+e^{x+e^x} \left (2 x^2-x+10\right )-e^{e^x}-e^{x+8}-2 e^{x+e^x+4}-e^{x+2 e^x}+5 \left (1-\frac {e^4}{5}\right )\right ) \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {x^2 \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}-\frac {\exp \left (e^x-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}+\frac {\left (5-e^4\right ) \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}+\frac {\left (-x^4+2 x^3+2 e^{e^x} x^2-11 \left (1-\frac {2 e^4}{11}\right ) x^2-e^{e^x} x+10 \left (1-\frac {e^4}{5}\right ) x-e^{2 e^x}+10 \left (1-\frac {e^4}{5}\right ) e^{e^x}-25 \left (1+\frac {1}{25} e^4 \left (e^4-10\right )\right )\right ) \exp \left (x-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (-x^2-e^x \left (x^2-x+5\right )^2+2 e^{x+4} \left (x^2-x+5\right )+e^{x+e^x} \left (2 x^2-x+10\right )-e^{e^x}-e^{x+8}-2 e^{x+e^x+4}-e^{x+2 e^x}+5 \left (1-\frac {e^4}{5}\right )\right ) \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {x^2 \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}-\frac {\exp \left (e^x-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}+\frac {\left (5-e^4\right ) \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}+\frac {\left (-x^4+2 x^3+2 e^{e^x} x^2-11 \left (1-\frac {2 e^4}{11}\right ) x^2-e^{e^x} x+10 \left (1-\frac {e^4}{5}\right ) x-e^{2 e^x}+10 \left (1-\frac {e^4}{5}\right ) e^{e^x}-25 \left (1+\frac {1}{25} e^4 \left (e^4-10\right )\right )\right ) \exp \left (x-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (-x^2-e^x \left (x^2-x+5\right )^2+2 e^{x+4} \left (x^2-x+5\right )+e^{x+e^x} \left (2 x^2-x+10\right )-e^{e^x}-e^{x+8}-2 e^{x+e^x+4}-e^{x+2 e^x}+5 \left (1-\frac {e^4}{5}\right )\right ) \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {x^2 \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}-\frac {\exp \left (e^x-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}+\frac {\left (5-e^4\right ) \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}+\frac {\left (-x^4+2 x^3+2 e^{e^x} x^2-11 \left (1-\frac {2 e^4}{11}\right ) x^2-e^{e^x} x+10 \left (1-\frac {e^4}{5}\right ) x-e^{2 e^x}+10 \left (1-\frac {e^4}{5}\right ) e^{e^x}-25 \left (1+\frac {1}{25} e^4 \left (e^4-10\right )\right )\right ) \exp \left (x-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (-x^2-e^x \left (x^2-x+5\right )^2+2 e^{x+4} \left (x^2-x+5\right )+e^{x+e^x} \left (2 x^2-x+10\right )-e^{e^x}-e^{x+8}-2 e^{x+e^x+4}-e^{x+2 e^x}+5 \left (1-\frac {e^4}{5}\right )\right ) \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {x^2 \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}-\frac {\exp \left (e^x-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}+\frac {\left (5-e^4\right ) \exp \left (-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}+\frac {\left (-x^4+2 x^3+2 e^{e^x} x^2-11 \left (1-\frac {2 e^4}{11}\right ) x^2-e^{e^x} x+10 \left (1-\frac {e^4}{5}\right ) x-e^{2 e^x}+10 \left (1-\frac {e^4}{5}\right ) e^{e^x}-25 \left (1+\frac {1}{25} e^4 \left (e^4-10\right )\right )\right ) \exp \left (x-\frac {4 x^2+e^x \left (-x^2+x-5\right )-3 x-4 e^{e^x}+e^{x+4}+e^{x+e^x}+20 \left (1-\frac {e^4}{5}\right )}{-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )}\right )}{\left (-x^2+x+e^{e^x}-5 \left (1-\frac {e^4}{5}\right )\right )^2}\right )dx\) |
Int[(E^((-20 + 4*E^4 + E^E^x*(4 - E^x) + 3*x - 4*x^2 + E^x*(5 - E^4 - x + x^2))/(-5 + E^4 + E^E^x + x - x^2))*(5 - E^4 - E^(2*E^x + x) - x^2 + E^x*( -25 - E^8 + 10*x - 11*x^2 + 2*x^3 - x^4 + E^4*(10 - 2*x + 2*x^2)) + E^E^x* (-1 + E^x*(10 - 2*E^4 - x + 2*x^2))))/(25 + E^8 + E^(2*E^x) - 10*x + 11*x^ 2 - 2*x^3 + x^4 + E^4*(-10 + 2*x - 2*x^2) + E^E^x*(-10 + 2*E^4 + 2*x - 2*x ^2)),x]
3.15.80.3.1 Defintions of rubi rules used
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Time = 73.44 (sec) , antiderivative size = 57, normalized size of antiderivative = 1.73
| method | result | size |
| parallelrisch | \({\mathrm e}^{\frac {\left (-{\mathrm e}^{x}+4\right ) {\mathrm e}^{{\mathrm e}^{x}}+\left (-{\mathrm e}^{4}+x^{2}-x +5\right ) {\mathrm e}^{x}+4 \,{\mathrm e}^{4}-4 x^{2}+3 x -20}{{\mathrm e}^{{\mathrm e}^{x}}+{\mathrm e}^{4}-x^{2}+x -5}}\) | \(57\) |
int((-exp(x)*exp(exp(x))^2+((-2*exp(4)+2*x^2-x+10)*exp(x)-1)*exp(exp(x))+( -exp(4)^2+(2*x^2-2*x+10)*exp(4)-x^4+2*x^3-11*x^2+10*x-25)*exp(x)-exp(4)-x^ 2+5)*exp(((-exp(x)+4)*exp(exp(x))+(-exp(4)+x^2-x+5)*exp(x)+4*exp(4)-4*x^2+ 3*x-20)/(exp(exp(x))+exp(4)-x^2+x-5))/(exp(exp(x))^2+(2*exp(4)-2*x^2+2*x-1 0)*exp(exp(x))+exp(4)^2+(-2*x^2+2*x-10)*exp(4)+x^4-2*x^3+11*x^2-10*x+25),x ,method=_RETURNVERBOSE)
exp(((-exp(x)+4)*exp(exp(x))+(-exp(4)+x^2-x+5)*exp(x)+4*exp(4)-4*x^2+3*x-2 0)/(exp(exp(x))+exp(4)-x^2+x-5))
Leaf count of result is larger than twice the leaf count of optimal. 59 vs. \(2 (28) = 56\).
Time = 0.26 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.79 \[ \int \frac {e^{\frac {-20+4 e^4+e^{e^x} \left (4-e^x\right )+3 x-4 x^2+e^x \left (5-e^4-x+x^2\right )}{-5+e^4+e^{e^x}+x-x^2}} \left (5-e^4-e^{2 e^x+x}-x^2+e^x \left (-25-e^8+10 x-11 x^2+2 x^3-x^4+e^4 \left (10-2 x+2 x^2\right )\right )+e^{e^x} \left (-1+e^x \left (10-2 e^4-x+2 x^2\right )\right )\right )}{25+e^8+e^{2 e^x}-10 x+11 x^2-2 x^3+x^4+e^4 \left (-10+2 x-2 x^2\right )+e^{e^x} \left (-10+2 e^4+2 x-2 x^2\right )} \, dx=e^{\left (\frac {4 \, x^{2} - {\left (x^{2} - x - e^{4} + 5\right )} e^{x} + {\left (e^{x} - 4\right )} e^{\left (e^{x}\right )} - 3 \, x - 4 \, e^{4} + 20}{x^{2} - x - e^{4} - e^{\left (e^{x}\right )} + 5}\right )} \]
integrate((-exp(x)*exp(exp(x))^2+((-2*exp(4)+2*x^2-x+10)*exp(x)-1)*exp(exp (x))+(-exp(4)^2+(2*x^2-2*x+10)*exp(4)-x^4+2*x^3-11*x^2+10*x-25)*exp(x)-exp (4)-x^2+5)*exp(((-exp(x)+4)*exp(exp(x))+(-exp(4)+x^2-x+5)*exp(x)+4*exp(4)- 4*x^2+3*x-20)/(exp(exp(x))+exp(4)-x^2+x-5))/(exp(exp(x))^2+(2*exp(4)-2*x^2 +2*x-10)*exp(exp(x))+exp(4)^2+(-2*x^2+2*x-10)*exp(4)+x^4-2*x^3+11*x^2-10*x +25),x, algorithm=\
e^((4*x^2 - (x^2 - x - e^4 + 5)*e^x + (e^x - 4)*e^(e^x) - 3*x - 4*e^4 + 20 )/(x^2 - x - e^4 - e^(e^x) + 5))
Leaf count of result is larger than twice the leaf count of optimal. 54 vs. \(2 (22) = 44\).
Time = 1.16 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.64 \[ \int \frac {e^{\frac {-20+4 e^4+e^{e^x} \left (4-e^x\right )+3 x-4 x^2+e^x \left (5-e^4-x+x^2\right )}{-5+e^4+e^{e^x}+x-x^2}} \left (5-e^4-e^{2 e^x+x}-x^2+e^x \left (-25-e^8+10 x-11 x^2+2 x^3-x^4+e^4 \left (10-2 x+2 x^2\right )\right )+e^{e^x} \left (-1+e^x \left (10-2 e^4-x+2 x^2\right )\right )\right )}{25+e^8+e^{2 e^x}-10 x+11 x^2-2 x^3+x^4+e^4 \left (-10+2 x-2 x^2\right )+e^{e^x} \left (-10+2 e^4+2 x-2 x^2\right )} \, dx=e^{\frac {- 4 x^{2} + 3 x + \left (4 - e^{x}\right ) e^{e^{x}} + \left (x^{2} - x - e^{4} + 5\right ) e^{x} - 20 + 4 e^{4}}{- x^{2} + x + e^{e^{x}} - 5 + e^{4}}} \]
integrate((-exp(x)*exp(exp(x))**2+((-2*exp(4)+2*x**2-x+10)*exp(x)-1)*exp(e xp(x))+(-exp(4)**2+(2*x**2-2*x+10)*exp(4)-x**4+2*x**3-11*x**2+10*x-25)*exp (x)-exp(4)-x**2+5)*exp(((-exp(x)+4)*exp(exp(x))+(-exp(4)+x**2-x+5)*exp(x)+ 4*exp(4)-4*x**2+3*x-20)/(exp(exp(x))+exp(4)-x**2+x-5))/(exp(exp(x))**2+(2* exp(4)-2*x**2+2*x-10)*exp(exp(x))+exp(4)**2+(-2*x**2+2*x-10)*exp(4)+x**4-2 *x**3+11*x**2-10*x+25),x)
exp((-4*x**2 + 3*x + (4 - exp(x))*exp(exp(x)) + (x**2 - x - exp(4) + 5)*ex p(x) - 20 + 4*exp(4))/(-x**2 + x + exp(exp(x)) - 5 + exp(4)))
Time = 0.74 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.85 \[ \int \frac {e^{\frac {-20+4 e^4+e^{e^x} \left (4-e^x\right )+3 x-4 x^2+e^x \left (5-e^4-x+x^2\right )}{-5+e^4+e^{e^x}+x-x^2}} \left (5-e^4-e^{2 e^x+x}-x^2+e^x \left (-25-e^8+10 x-11 x^2+2 x^3-x^4+e^4 \left (10-2 x+2 x^2\right )\right )+e^{e^x} \left (-1+e^x \left (10-2 e^4-x+2 x^2\right )\right )\right )}{25+e^8+e^{2 e^x}-10 x+11 x^2-2 x^3+x^4+e^4 \left (-10+2 x-2 x^2\right )+e^{e^x} \left (-10+2 e^4+2 x-2 x^2\right )} \, dx=e^{\left (\frac {x}{x^{2} - x - e^{4} - e^{\left (e^{x}\right )} + 5} - e^{x} + 4\right )} \]
integrate((-exp(x)*exp(exp(x))^2+((-2*exp(4)+2*x^2-x+10)*exp(x)-1)*exp(exp (x))+(-exp(4)^2+(2*x^2-2*x+10)*exp(4)-x^4+2*x^3-11*x^2+10*x-25)*exp(x)-exp (4)-x^2+5)*exp(((-exp(x)+4)*exp(exp(x))+(-exp(4)+x^2-x+5)*exp(x)+4*exp(4)- 4*x^2+3*x-20)/(exp(exp(x))+exp(4)-x^2+x-5))/(exp(exp(x))^2+(2*exp(4)-2*x^2 +2*x-10)*exp(exp(x))+exp(4)^2+(-2*x^2+2*x-10)*exp(4)+x^4-2*x^3+11*x^2-10*x +25),x, algorithm=\
\[ \int \frac {e^{\frac {-20+4 e^4+e^{e^x} \left (4-e^x\right )+3 x-4 x^2+e^x \left (5-e^4-x+x^2\right )}{-5+e^4+e^{e^x}+x-x^2}} \left (5-e^4-e^{2 e^x+x}-x^2+e^x \left (-25-e^8+10 x-11 x^2+2 x^3-x^4+e^4 \left (10-2 x+2 x^2\right )\right )+e^{e^x} \left (-1+e^x \left (10-2 e^4-x+2 x^2\right )\right )\right )}{25+e^8+e^{2 e^x}-10 x+11 x^2-2 x^3+x^4+e^4 \left (-10+2 x-2 x^2\right )+e^{e^x} \left (-10+2 e^4+2 x-2 x^2\right )} \, dx=\int { -\frac {{\left (x^{2} + {\left (x^{4} - 2 \, x^{3} + 11 \, x^{2} - 2 \, {\left (x^{2} - x + 5\right )} e^{4} - 10 \, x + e^{8} + 25\right )} e^{x} - {\left ({\left (2 \, x^{2} - x - 2 \, e^{4} + 10\right )} e^{x} - 1\right )} e^{\left (e^{x}\right )} + e^{4} + e^{\left (x + 2 \, e^{x}\right )} - 5\right )} e^{\left (\frac {4 \, x^{2} - {\left (x^{2} - x - e^{4} + 5\right )} e^{x} + {\left (e^{x} - 4\right )} e^{\left (e^{x}\right )} - 3 \, x - 4 \, e^{4} + 20}{x^{2} - x - e^{4} - e^{\left (e^{x}\right )} + 5}\right )}}{x^{4} - 2 \, x^{3} + 11 \, x^{2} - 2 \, {\left (x^{2} - x + 5\right )} e^{4} - 2 \, {\left (x^{2} - x - e^{4} + 5\right )} e^{\left (e^{x}\right )} - 10 \, x + e^{8} + e^{\left (2 \, e^{x}\right )} + 25} \,d x } \]
integrate((-exp(x)*exp(exp(x))^2+((-2*exp(4)+2*x^2-x+10)*exp(x)-1)*exp(exp (x))+(-exp(4)^2+(2*x^2-2*x+10)*exp(4)-x^4+2*x^3-11*x^2+10*x-25)*exp(x)-exp (4)-x^2+5)*exp(((-exp(x)+4)*exp(exp(x))+(-exp(4)+x^2-x+5)*exp(x)+4*exp(4)- 4*x^2+3*x-20)/(exp(exp(x))+exp(4)-x^2+x-5))/(exp(exp(x))^2+(2*exp(4)-2*x^2 +2*x-10)*exp(exp(x))+exp(4)^2+(-2*x^2+2*x-10)*exp(4)+x^4-2*x^3+11*x^2-10*x +25),x, algorithm=\
integrate(-(x^2 + (x^4 - 2*x^3 + 11*x^2 - 2*(x^2 - x + 5)*e^4 - 10*x + e^8 + 25)*e^x - ((2*x^2 - x - 2*e^4 + 10)*e^x - 1)*e^(e^x) + e^4 + e^(x + 2*e ^x) - 5)*e^((4*x^2 - (x^2 - x - e^4 + 5)*e^x + (e^x - 4)*e^(e^x) - 3*x - 4 *e^4 + 20)/(x^2 - x - e^4 - e^(e^x) + 5))/(x^4 - 2*x^3 + 11*x^2 - 2*(x^2 - x + 5)*e^4 - 2*(x^2 - x - e^4 + 5)*e^(e^x) - 10*x + e^8 + e^(2*e^x) + 25) , x)
Time = 9.88 (sec) , antiderivative size = 208, normalized size of antiderivative = 6.30 \[ \int \frac {e^{\frac {-20+4 e^4+e^{e^x} \left (4-e^x\right )+3 x-4 x^2+e^x \left (5-e^4-x+x^2\right )}{-5+e^4+e^{e^x}+x-x^2}} \left (5-e^4-e^{2 e^x+x}-x^2+e^x \left (-25-e^8+10 x-11 x^2+2 x^3-x^4+e^4 \left (10-2 x+2 x^2\right )\right )+e^{e^x} \left (-1+e^x \left (10-2 e^4-x+2 x^2\right )\right )\right )}{25+e^8+e^{2 e^x}-10 x+11 x^2-2 x^3+x^4+e^4 \left (-10+2 x-2 x^2\right )+e^{e^x} \left (-10+2 e^4+2 x-2 x^2\right )} \, dx={\mathrm {e}}^{\frac {4\,{\mathrm {e}}^{{\mathrm {e}}^x}}{x+{\mathrm {e}}^{{\mathrm {e}}^x}+{\mathrm {e}}^4-x^2-5}}\,{\mathrm {e}}^{-\frac {{\mathrm {e}}^4\,{\mathrm {e}}^x}{x+{\mathrm {e}}^{{\mathrm {e}}^x}+{\mathrm {e}}^4-x^2-5}}\,{\mathrm {e}}^{-\frac {x\,{\mathrm {e}}^x}{x+{\mathrm {e}}^{{\mathrm {e}}^x}+{\mathrm {e}}^4-x^2-5}}\,{\mathrm {e}}^{\frac {4\,{\mathrm {e}}^4}{x+{\mathrm {e}}^{{\mathrm {e}}^x}+{\mathrm {e}}^4-x^2-5}}\,{\mathrm {e}}^{\frac {3\,x}{x+{\mathrm {e}}^{{\mathrm {e}}^x}+{\mathrm {e}}^4-x^2-5}}\,{\mathrm {e}}^{\frac {x^2\,{\mathrm {e}}^x}{x+{\mathrm {e}}^{{\mathrm {e}}^x}+{\mathrm {e}}^4-x^2-5}}\,{\mathrm {e}}^{-\frac {4\,x^2}{x+{\mathrm {e}}^{{\mathrm {e}}^x}+{\mathrm {e}}^4-x^2-5}}\,{\mathrm {e}}^{\frac {5\,{\mathrm {e}}^x}{x+{\mathrm {e}}^{{\mathrm {e}}^x}+{\mathrm {e}}^4-x^2-5}}\,{\mathrm {e}}^{-\frac {20}{x+{\mathrm {e}}^{{\mathrm {e}}^x}+{\mathrm {e}}^4-x^2-5}}\,{\mathrm {e}}^{-\frac {{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^x}{x+{\mathrm {e}}^{{\mathrm {e}}^x}+{\mathrm {e}}^4-x^2-5}} \]
int(-(exp(-(exp(x)*(x + exp(4) - x^2 - 5) - 4*exp(4) - 3*x + 4*x^2 + exp(e xp(x))*(exp(x) - 4) + 20)/(x + exp(exp(x)) + exp(4) - x^2 - 5))*(exp(4) + exp(exp(x))*(exp(x)*(x + 2*exp(4) - 2*x^2 - 10) + 1) + exp(x)*(exp(8) - 10 *x - exp(4)*(2*x^2 - 2*x + 10) + 11*x^2 - 2*x^3 + x^4 + 25) + x^2 + exp(2* exp(x))*exp(x) - 5))/(exp(8) - 10*x + exp(2*exp(x)) - exp(4)*(2*x^2 - 2*x + 10) + exp(exp(x))*(2*x + 2*exp(4) - 2*x^2 - 10) + 11*x^2 - 2*x^3 + x^4 + 25),x)
exp((4*exp(exp(x)))/(x + exp(exp(x)) + exp(4) - x^2 - 5))*exp(-(exp(4)*exp (x))/(x + exp(exp(x)) + exp(4) - x^2 - 5))*exp(-(x*exp(x))/(x + exp(exp(x) ) + exp(4) - x^2 - 5))*exp((4*exp(4))/(x + exp(exp(x)) + exp(4) - x^2 - 5) )*exp((3*x)/(x + exp(exp(x)) + exp(4) - x^2 - 5))*exp((x^2*exp(x))/(x + ex p(exp(x)) + exp(4) - x^2 - 5))*exp(-(4*x^2)/(x + exp(exp(x)) + exp(4) - x^ 2 - 5))*exp((5*exp(x))/(x + exp(exp(x)) + exp(4) - x^2 - 5))*exp(-20/(x + exp(exp(x)) + exp(4) - x^2 - 5))*exp(-(exp(exp(x))*exp(x))/(x + exp(exp(x) ) + exp(4) - x^2 - 5))