Integrand size = 238, antiderivative size = 32 \[ \int \frac {e^{\frac {8-6 x+5 x^2-x^3-x^4+e^{4 e^{x^2} x} \left (4-5 x+x^2+x^3\right )}{e^{4 e^{x^2} x} (-4+x)+4 x-x^2}} \left (-32+16 x+14 x^2-8 x^3-11 x^4+2 x^5+e^{8 e^{x^2} x} \left (16-8 x-11 x^2+2 x^3\right )+e^{4 e^{x^2} x} \left (-32 x+16 x^2+22 x^3-4 x^4+e^{x^2} \left (128-64 x+264 x^2-128 x^3+16 x^4\right )\right )\right )}{16 x^2-8 x^3+x^4+e^{8 e^{x^2} x} \left (16-8 x+x^2\right )+e^{4 e^{x^2} x} \left (-32 x+16 x^2-2 x^3\right )} \, dx=e^{-1-\frac {2}{e^{4 e^{x^2} x}-x}+x+\frac {x^3}{-4+x}} \] Output:
exp(x^3/(-4+x)+x-2/(exp(4*exp(x^2)*x)-x)-1)
Time = 0.30 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.09 \[ \int \frac {e^{\frac {8-6 x+5 x^2-x^3-x^4+e^{4 e^{x^2} x} \left (4-5 x+x^2+x^3\right )}{e^{4 e^{x^2} x} (-4+x)+4 x-x^2}} \left (-32+16 x+14 x^2-8 x^3-11 x^4+2 x^5+e^{8 e^{x^2} x} \left (16-8 x-11 x^2+2 x^3\right )+e^{4 e^{x^2} x} \left (-32 x+16 x^2+22 x^3-4 x^4+e^{x^2} \left (128-64 x+264 x^2-128 x^3+16 x^4\right )\right )\right )}{16 x^2-8 x^3+x^4+e^{8 e^{x^2} x} \left (16-8 x+x^2\right )+e^{4 e^{x^2} x} \left (-32 x+16 x^2-2 x^3\right )} \, dx=e^{15-\frac {2}{e^{4 e^{x^2} x}-x}+\frac {64}{-4+x}+5 x+x^2} \] Input:
Integrate[(E^((8 - 6*x + 5*x^2 - x^3 - x^4 + E^(4*E^x^2*x)*(4 - 5*x + x^2 + x^3))/(E^(4*E^x^2*x)*(-4 + x) + 4*x - x^2))*(-32 + 16*x + 14*x^2 - 8*x^3 - 11*x^4 + 2*x^5 + E^(8*E^x^2*x)*(16 - 8*x - 11*x^2 + 2*x^3) + E^(4*E^x^2 *x)*(-32*x + 16*x^2 + 22*x^3 - 4*x^4 + E^x^2*(128 - 64*x + 264*x^2 - 128*x ^3 + 16*x^4))))/(16*x^2 - 8*x^3 + x^4 + E^(8*E^x^2*x)*(16 - 8*x + x^2) + E ^(4*E^x^2*x)*(-32*x + 16*x^2 - 2*x^3)),x]
Output:
E^(15 - 2/(E^(4*E^x^2*x) - x) + 64/(-4 + x) + 5*x + x^2)
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.
| \(\displaystyle \int \frac {\left (2 x^5-11 x^4-8 x^3+14 x^2+e^{8 e^{x^2} x} \left (2 x^3-11 x^2-8 x+16\right )+e^{4 e^{x^2} x} \left (-4 x^4+22 x^3+16 x^2+e^{x^2} \left (16 x^4-128 x^3+264 x^2-64 x+128\right )-32 x\right )+16 x-32\right ) \exp \left (\frac {-x^4-x^3+5 x^2+e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-6 x+8}{-x^2+e^{4 e^{x^2} x} (x-4)+4 x}\right )}{x^4-8 x^3+16 x^2+e^{8 e^{x^2} x} \left (x^2-8 x+16\right )+e^{4 e^{x^2} x} \left (-2 x^3+16 x^2-32 x\right )} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {\left (2 x^5-11 x^4-8 x^3+14 x^2+e^{8 e^{x^2} x} \left (2 x^3-11 x^2-8 x+16\right )+e^{4 e^{x^2} x} \left (-4 x^4+22 x^3+16 x^2+e^{x^2} \left (16 x^4-128 x^3+264 x^2-64 x+128\right )-32 x\right )+16 x-32\right ) \exp \left (\frac {-x^4-x^3+5 x^2+e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-6 x+8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}\right )}{(4-x)^2 \left (e^{4 e^{x^2} x}-x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 e^{\frac {-x^4-x^3+5 x^2-6 x+e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )+8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^5}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {11 e^{\frac {-x^4-x^3+5 x^2-6 x+e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )+8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^4}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {4 e^{4 e^{x^2} x+\frac {-x^4-x^3+5 x^2-6 x+e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )+8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^4}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {8 e^{\frac {-x^4-x^3+5 x^2-6 x+e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )+8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^3}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {22 e^{4 e^{x^2} x+\frac {-x^4-x^3+5 x^2-6 x+e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )+8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^3}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {14 e^{\frac {-x^4-x^3+5 x^2-6 x+e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )+8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^2}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {16 e^{4 e^{x^2} x+\frac {-x^4-x^3+5 x^2-6 x+e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )+8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^2}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {16 e^{\frac {-x^4-x^3+5 x^2-6 x+e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )+8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {32 e^{4 e^{x^2} x+\frac {-x^4-x^3+5 x^2-6 x+e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )+8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {8 e^{x^2+4 e^{x^2} x+\frac {-x^4-x^3+5 x^2-6 x+e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )+8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^2+1\right )}{\left (e^{4 e^{x^2} x}-x\right )^2}+\frac {e^{8 e^{x^2} x+\frac {-x^4-x^3+5 x^2-6 x+e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )+8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^3-11 x^2-8 x+16\right )}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {32 e^{\frac {-x^4-x^3+5 x^2-6 x+e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )+8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}}}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (2 x^5-11 x^4-8 x^3+14 x^2+8 e^{x \left (4 e^{x^2}+x\right )} (x-4)^2 \left (2 x^2+1\right )-2 e^{4 e^{x^2} x} \left (2 x^3-11 x^2-8 x+16\right ) x+e^{8 e^{x^2} x} \left (2 x^3-11 x^2-8 x+16\right )+16 x-32\right ) \exp \left (-\frac {x^4+x^3-5 x^2-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )+6 x-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}\right )}{(4-x)^2 \left (e^{4 e^{x^2} x}-x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^5}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {11 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^4}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {8 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^3}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {14 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^2}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {2 e^{4 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^3-11 x^2-8 x+16\right ) x}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {16 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {8 e^{x^2+4 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^2+1\right )}{\left (e^{4 e^{x^2} x}-x\right )^2}+\frac {e^{8 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^3-11 x^2-8 x+16\right )}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {32 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}}}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (2 x^5-11 x^4-8 x^3+14 x^2+8 e^{x \left (4 e^{x^2}+x\right )} (x-4)^2 \left (2 x^2+1\right )-2 e^{4 e^{x^2} x} \left (2 x^3-11 x^2-8 x+16\right ) x+e^{8 e^{x^2} x} \left (2 x^3-11 x^2-8 x+16\right )+16 x-32\right ) \exp \left (-\frac {x^4+x^3-5 x^2-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )+6 x-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}\right )}{(4-x)^2 \left (e^{4 e^{x^2} x}-x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^5}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {11 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^4}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {8 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^3}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {14 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^2}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {2 e^{4 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^3-11 x^2-8 x+16\right ) x}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {16 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {8 e^{x^2+4 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^2+1\right )}{\left (e^{4 e^{x^2} x}-x\right )^2}+\frac {e^{8 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^3-11 x^2-8 x+16\right )}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {32 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}}}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (2 x^5-11 x^4-8 x^3+14 x^2+8 e^{x \left (4 e^{x^2}+x\right )} (x-4)^2 \left (2 x^2+1\right )-2 e^{4 e^{x^2} x} \left (2 x^3-11 x^2-8 x+16\right ) x+e^{8 e^{x^2} x} \left (2 x^3-11 x^2-8 x+16\right )+16 x-32\right ) \exp \left (-\frac {x^4+x^3-5 x^2-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )+6 x-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}\right )}{(4-x)^2 \left (e^{4 e^{x^2} x}-x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^5}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {11 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^4}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {8 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^3}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {14 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^2}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {2 e^{4 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^3-11 x^2-8 x+16\right ) x}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {16 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {8 e^{x^2+4 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^2+1\right )}{\left (e^{4 e^{x^2} x}-x\right )^2}+\frac {e^{8 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^3-11 x^2-8 x+16\right )}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {32 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}}}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (2 x^5-11 x^4-8 x^3+14 x^2+8 e^{x \left (4 e^{x^2}+x\right )} (x-4)^2 \left (2 x^2+1\right )-2 e^{4 e^{x^2} x} \left (2 x^3-11 x^2-8 x+16\right ) x+e^{8 e^{x^2} x} \left (2 x^3-11 x^2-8 x+16\right )+16 x-32\right ) \exp \left (-\frac {x^4+x^3-5 x^2-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )+6 x-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}\right )}{(4-x)^2 \left (e^{4 e^{x^2} x}-x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^5}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {11 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^4}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {8 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^3}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {14 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^2}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {2 e^{4 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^3-11 x^2-8 x+16\right ) x}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {16 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {8 e^{x^2+4 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^2+1\right )}{\left (e^{4 e^{x^2} x}-x\right )^2}+\frac {e^{8 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^3-11 x^2-8 x+16\right )}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {32 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}}}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (2 x^5-11 x^4-8 x^3+14 x^2+8 e^{x \left (4 e^{x^2}+x\right )} (x-4)^2 \left (2 x^2+1\right )-2 e^{4 e^{x^2} x} \left (2 x^3-11 x^2-8 x+16\right ) x+e^{8 e^{x^2} x} \left (2 x^3-11 x^2-8 x+16\right )+16 x-32\right ) \exp \left (-\frac {x^4+x^3-5 x^2-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )+6 x-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}\right )}{(4-x)^2 \left (e^{4 e^{x^2} x}-x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^5}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {11 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^4}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {8 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^3}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {14 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^2}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {2 e^{4 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^3-11 x^2-8 x+16\right ) x}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {16 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {8 e^{x^2+4 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^2+1\right )}{\left (e^{4 e^{x^2} x}-x\right )^2}+\frac {e^{8 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^3-11 x^2-8 x+16\right )}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {32 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}}}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (2 x^5-11 x^4-8 x^3+14 x^2+8 e^{x \left (4 e^{x^2}+x\right )} (x-4)^2 \left (2 x^2+1\right )-2 e^{4 e^{x^2} x} \left (2 x^3-11 x^2-8 x+16\right ) x+e^{8 e^{x^2} x} \left (2 x^3-11 x^2-8 x+16\right )+16 x-32\right ) \exp \left (-\frac {x^4+x^3-5 x^2-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )+6 x-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}\right )}{(4-x)^2 \left (e^{4 e^{x^2} x}-x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^5}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {11 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^4}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {8 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^3}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {14 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^2}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {2 e^{4 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^3-11 x^2-8 x+16\right ) x}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {16 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {8 e^{x^2+4 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^2+1\right )}{\left (e^{4 e^{x^2} x}-x\right )^2}+\frac {e^{8 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^3-11 x^2-8 x+16\right )}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {32 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}}}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (2 x^5-11 x^4-8 x^3+14 x^2+8 e^{x \left (4 e^{x^2}+x\right )} (x-4)^2 \left (2 x^2+1\right )-2 e^{4 e^{x^2} x} \left (2 x^3-11 x^2-8 x+16\right ) x+e^{8 e^{x^2} x} \left (2 x^3-11 x^2-8 x+16\right )+16 x-32\right ) \exp \left (-\frac {x^4+x^3-5 x^2-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )+6 x-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}\right )}{(4-x)^2 \left (e^{4 e^{x^2} x}-x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^5}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {11 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^4}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {8 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^3}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {14 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^2}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {2 e^{4 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^3-11 x^2-8 x+16\right ) x}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {16 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {8 e^{x^2+4 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^2+1\right )}{\left (e^{4 e^{x^2} x}-x\right )^2}+\frac {e^{8 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^3-11 x^2-8 x+16\right )}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {32 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}}}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (2 x^5-11 x^4-8 x^3+14 x^2+8 e^{x \left (4 e^{x^2}+x\right )} (x-4)^2 \left (2 x^2+1\right )-2 e^{4 e^{x^2} x} \left (2 x^3-11 x^2-8 x+16\right ) x+e^{8 e^{x^2} x} \left (2 x^3-11 x^2-8 x+16\right )+16 x-32\right ) \exp \left (-\frac {x^4+x^3-5 x^2-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )+6 x-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}\right )}{(4-x)^2 \left (e^{4 e^{x^2} x}-x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^5}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {11 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^4}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {8 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^3}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {14 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^2}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {2 e^{4 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^3-11 x^2-8 x+16\right ) x}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {16 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {8 e^{x^2+4 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^2+1\right )}{\left (e^{4 e^{x^2} x}-x\right )^2}+\frac {e^{8 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^3-11 x^2-8 x+16\right )}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {32 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}}}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (2 x^5-11 x^4-8 x^3+14 x^2+8 e^{x \left (4 e^{x^2}+x\right )} (x-4)^2 \left (2 x^2+1\right )-2 e^{4 e^{x^2} x} \left (2 x^3-11 x^2-8 x+16\right ) x+e^{8 e^{x^2} x} \left (2 x^3-11 x^2-8 x+16\right )+16 x-32\right ) \exp \left (-\frac {x^4+x^3-5 x^2-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )+6 x-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}\right )}{(4-x)^2 \left (e^{4 e^{x^2} x}-x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^5}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {11 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^4}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {8 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^3}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {14 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^2}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {2 e^{4 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^3-11 x^2-8 x+16\right ) x}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {16 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {8 e^{x^2+4 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^2+1\right )}{\left (e^{4 e^{x^2} x}-x\right )^2}+\frac {e^{8 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^3-11 x^2-8 x+16\right )}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {32 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}}}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (2 x^5-11 x^4-8 x^3+14 x^2+8 e^{x \left (4 e^{x^2}+x\right )} (x-4)^2 \left (2 x^2+1\right )-2 e^{4 e^{x^2} x} \left (2 x^3-11 x^2-8 x+16\right ) x+e^{8 e^{x^2} x} \left (2 x^3-11 x^2-8 x+16\right )+16 x-32\right ) \exp \left (-\frac {x^4+x^3-5 x^2-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )+6 x-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}\right )}{(4-x)^2 \left (e^{4 e^{x^2} x}-x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^5}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {11 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^4}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {8 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^3}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {14 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^2}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {2 e^{4 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^3-11 x^2-8 x+16\right ) x}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {16 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {8 e^{x^2+4 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^2+1\right )}{\left (e^{4 e^{x^2} x}-x\right )^2}+\frac {e^{8 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^3-11 x^2-8 x+16\right )}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {32 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}}}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (2 x^5-11 x^4-8 x^3+14 x^2+8 e^{x \left (4 e^{x^2}+x\right )} (x-4)^2 \left (2 x^2+1\right )-2 e^{4 e^{x^2} x} \left (2 x^3-11 x^2-8 x+16\right ) x+e^{8 e^{x^2} x} \left (2 x^3-11 x^2-8 x+16\right )+16 x-32\right ) \exp \left (-\frac {x^4+x^3-5 x^2-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )+6 x-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}\right )}{(4-x)^2 \left (e^{4 e^{x^2} x}-x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^5}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {11 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^4}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {8 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^3}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {14 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^2}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {2 e^{4 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^3-11 x^2-8 x+16\right ) x}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {16 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {8 e^{x^2+4 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^2+1\right )}{\left (e^{4 e^{x^2} x}-x\right )^2}+\frac {e^{8 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^3-11 x^2-8 x+16\right )}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {32 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}}}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (2 x^5-11 x^4-8 x^3+14 x^2+8 e^{x \left (4 e^{x^2}+x\right )} (x-4)^2 \left (2 x^2+1\right )-2 e^{4 e^{x^2} x} \left (2 x^3-11 x^2-8 x+16\right ) x+e^{8 e^{x^2} x} \left (2 x^3-11 x^2-8 x+16\right )+16 x-32\right ) \exp \left (-\frac {x^4+x^3-5 x^2-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )+6 x-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}\right )}{(4-x)^2 \left (e^{4 e^{x^2} x}-x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^5}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {11 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^4}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {8 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^3}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {14 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^2}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {2 e^{4 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^3-11 x^2-8 x+16\right ) x}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {16 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {8 e^{x^2+4 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^2+1\right )}{\left (e^{4 e^{x^2} x}-x\right )^2}+\frac {e^{8 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^3-11 x^2-8 x+16\right )}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {32 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}}}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (2 x^5-11 x^4-8 x^3+14 x^2+8 e^{x \left (4 e^{x^2}+x\right )} (x-4)^2 \left (2 x^2+1\right )-2 e^{4 e^{x^2} x} \left (2 x^3-11 x^2-8 x+16\right ) x+e^{8 e^{x^2} x} \left (2 x^3-11 x^2-8 x+16\right )+16 x-32\right ) \exp \left (-\frac {x^4+x^3-5 x^2-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )+6 x-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}\right )}{(4-x)^2 \left (e^{4 e^{x^2} x}-x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^5}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {11 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^4}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {8 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^3}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {14 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^2}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {2 e^{4 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^3-11 x^2-8 x+16\right ) x}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {16 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {8 e^{x^2+4 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^2+1\right )}{\left (e^{4 e^{x^2} x}-x\right )^2}+\frac {e^{8 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^3-11 x^2-8 x+16\right )}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {32 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}}}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (2 x^5-11 x^4-8 x^3+14 x^2+8 e^{x \left (4 e^{x^2}+x\right )} (x-4)^2 \left (2 x^2+1\right )-2 e^{4 e^{x^2} x} \left (2 x^3-11 x^2-8 x+16\right ) x+e^{8 e^{x^2} x} \left (2 x^3-11 x^2-8 x+16\right )+16 x-32\right ) \exp \left (-\frac {x^4+x^3-5 x^2-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )+6 x-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}\right )}{(4-x)^2 \left (e^{4 e^{x^2} x}-x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^5}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {11 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^4}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {8 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^3}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {14 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x^2}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {2 e^{4 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^3-11 x^2-8 x+16\right ) x}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {16 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} x}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}+\frac {8 e^{x^2+4 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^2+1\right )}{\left (e^{4 e^{x^2} x}-x\right )^2}+\frac {e^{8 e^{x^2} x-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}} \left (2 x^3-11 x^2-8 x+16\right )}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}-\frac {32 e^{-\frac {x^4+x^3-5 x^2+6 x-e^{4 e^{x^2} x} \left (x^3+x^2-5 x+4\right )-8}{\left (e^{4 e^{x^2} x}-x\right ) (x-4)}}}{\left (e^{4 e^{x^2} x}-x\right )^2 (x-4)^2}\right )dx\) |
Input:
Int[(E^((8 - 6*x + 5*x^2 - x^3 - x^4 + E^(4*E^x^2*x)*(4 - 5*x + x^2 + x^3) )/(E^(4*E^x^2*x)*(-4 + x) + 4*x - x^2))*(-32 + 16*x + 14*x^2 - 8*x^3 - 11* x^4 + 2*x^5 + E^(8*E^x^2*x)*(16 - 8*x - 11*x^2 + 2*x^3) + E^(4*E^x^2*x)*(- 32*x + 16*x^2 + 22*x^3 - 4*x^4 + E^x^2*(128 - 64*x + 264*x^2 - 128*x^3 + 1 6*x^4))))/(16*x^2 - 8*x^3 + x^4 + E^(8*E^x^2*x)*(16 - 8*x + x^2) + E^(4*E^ x^2*x)*(-32*x + 16*x^2 - 2*x^3)),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(73\) vs. \(2(29)=58\).
Time = 117.06 (sec) , antiderivative size = 74, normalized size of antiderivative = 2.31
| method | result | size |
| parallelrisch | \({\mathrm e}^{\frac {\left (x^{3}+x^{2}-5 x +4\right ) {\mathrm e}^{4 \,{\mathrm e}^{x^{2}} x}-x^{4}-x^{3}+5 x^{2}-6 x +8}{{\mathrm e}^{4 \,{\mathrm e}^{x^{2}} x} x -x^{2}-4 \,{\mathrm e}^{4 \,{\mathrm e}^{x^{2}} x}+4 x}}\) | \(74\) |
| risch | \({\mathrm e}^{\frac {-{\mathrm e}^{4 \,{\mathrm e}^{x^{2}} x} x^{3}+x^{4}-{\mathrm e}^{4 \,{\mathrm e}^{x^{2}} x} x^{2}+x^{3}+5 \,{\mathrm e}^{4 \,{\mathrm e}^{x^{2}} x} x -5 x^{2}-4 \,{\mathrm e}^{4 \,{\mathrm e}^{x^{2}} x}+6 x -8}{\left (x -4\right ) \left (-{\mathrm e}^{4 \,{\mathrm e}^{x^{2}} x}+x \right )}}\) | \(85\) |
Input:
int(((2*x^3-11*x^2-8*x+16)*exp(4*exp(x^2)*x)^2+((16*x^4-128*x^3+264*x^2-64 *x+128)*exp(x^2)-4*x^4+22*x^3+16*x^2-32*x)*exp(4*exp(x^2)*x)+2*x^5-11*x^4- 8*x^3+14*x^2+16*x-32)*exp(((x^3+x^2-5*x+4)*exp(4*exp(x^2)*x)-x^4-x^3+5*x^2 -6*x+8)/((x-4)*exp(4*exp(x^2)*x)-x^2+4*x))/((x^2-8*x+16)*exp(4*exp(x^2)*x) ^2+(-2*x^3+16*x^2-32*x)*exp(4*exp(x^2)*x)+x^4-8*x^3+16*x^2),x,method=_RETU RNVERBOSE)
Output:
exp(((x^3+x^2-5*x+4)*exp(4*exp(x^2)*x)-x^4-x^3+5*x^2-6*x+8)/(exp(4*exp(x^2 )*x)*x-x^2-4*exp(4*exp(x^2)*x)+4*x))
Leaf count of result is larger than twice the leaf count of optimal. 61 vs. \(2 (29) = 58\).
Time = 0.08 (sec) , antiderivative size = 61, normalized size of antiderivative = 1.91 \[ \int \frac {e^{\frac {8-6 x+5 x^2-x^3-x^4+e^{4 e^{x^2} x} \left (4-5 x+x^2+x^3\right )}{e^{4 e^{x^2} x} (-4+x)+4 x-x^2}} \left (-32+16 x+14 x^2-8 x^3-11 x^4+2 x^5+e^{8 e^{x^2} x} \left (16-8 x-11 x^2+2 x^3\right )+e^{4 e^{x^2} x} \left (-32 x+16 x^2+22 x^3-4 x^4+e^{x^2} \left (128-64 x+264 x^2-128 x^3+16 x^4\right )\right )\right )}{16 x^2-8 x^3+x^4+e^{8 e^{x^2} x} \left (16-8 x+x^2\right )+e^{4 e^{x^2} x} \left (-32 x+16 x^2-2 x^3\right )} \, dx=e^{\left (\frac {x^{4} + x^{3} - 5 \, x^{2} - {\left (x^{3} + x^{2} - 5 \, x + 4\right )} e^{\left (4 \, x e^{\left (x^{2}\right )}\right )} + 6 \, x - 8}{x^{2} - {\left (x - 4\right )} e^{\left (4 \, x e^{\left (x^{2}\right )}\right )} - 4 \, x}\right )} \] Input:
integrate(((2*x^3-11*x^2-8*x+16)*exp(4*exp(x^2)*x)^2+((16*x^4-128*x^3+264* x^2-64*x+128)*exp(x^2)-4*x^4+22*x^3+16*x^2-32*x)*exp(4*exp(x^2)*x)+2*x^5-1 1*x^4-8*x^3+14*x^2+16*x-32)*exp(((x^3+x^2-5*x+4)*exp(4*exp(x^2)*x)-x^4-x^3 +5*x^2-6*x+8)/((-4+x)*exp(4*exp(x^2)*x)-x^2+4*x))/((x^2-8*x+16)*exp(4*exp( x^2)*x)^2+(-2*x^3+16*x^2-32*x)*exp(4*exp(x^2)*x)+x^4-8*x^3+16*x^2),x, algo rithm="fricas")
Output:
e^((x^4 + x^3 - 5*x^2 - (x^3 + x^2 - 5*x + 4)*e^(4*x*e^(x^2)) + 6*x - 8)/( x^2 - (x - 4)*e^(4*x*e^(x^2)) - 4*x))
Leaf count of result is larger than twice the leaf count of optimal. 60 vs. \(2 (24) = 48\).
Time = 2.46 (sec) , antiderivative size = 60, normalized size of antiderivative = 1.88 \[ \int \frac {e^{\frac {8-6 x+5 x^2-x^3-x^4+e^{4 e^{x^2} x} \left (4-5 x+x^2+x^3\right )}{e^{4 e^{x^2} x} (-4+x)+4 x-x^2}} \left (-32+16 x+14 x^2-8 x^3-11 x^4+2 x^5+e^{8 e^{x^2} x} \left (16-8 x-11 x^2+2 x^3\right )+e^{4 e^{x^2} x} \left (-32 x+16 x^2+22 x^3-4 x^4+e^{x^2} \left (128-64 x+264 x^2-128 x^3+16 x^4\right )\right )\right )}{16 x^2-8 x^3+x^4+e^{8 e^{x^2} x} \left (16-8 x+x^2\right )+e^{4 e^{x^2} x} \left (-32 x+16 x^2-2 x^3\right )} \, dx=e^{\frac {- x^{4} - x^{3} + 5 x^{2} - 6 x + \left (x^{3} + x^{2} - 5 x + 4\right ) e^{4 x e^{x^{2}}} + 8}{- x^{2} + 4 x + \left (x - 4\right ) e^{4 x e^{x^{2}}}}} \] Input:
integrate(((2*x**3-11*x**2-8*x+16)*exp(4*exp(x**2)*x)**2+((16*x**4-128*x** 3+264*x**2-64*x+128)*exp(x**2)-4*x**4+22*x**3+16*x**2-32*x)*exp(4*exp(x**2 )*x)+2*x**5-11*x**4-8*x**3+14*x**2+16*x-32)*exp(((x**3+x**2-5*x+4)*exp(4*e xp(x**2)*x)-x**4-x**3+5*x**2-6*x+8)/((-4+x)*exp(4*exp(x**2)*x)-x**2+4*x))/ ((x**2-8*x+16)*exp(4*exp(x**2)*x)**2+(-2*x**3+16*x**2-32*x)*exp(4*exp(x**2 )*x)+x**4-8*x**3+16*x**2),x)
Output:
exp((-x**4 - x**3 + 5*x**2 - 6*x + (x**3 + x**2 - 5*x + 4)*exp(4*x*exp(x** 2)) + 8)/(-x**2 + 4*x + (x - 4)*exp(4*x*exp(x**2))))
Leaf count of result is larger than twice the leaf count of optimal. 127 vs. \(2 (29) = 58\).
Time = 0.95 (sec) , antiderivative size = 127, normalized size of antiderivative = 3.97 \[ \int \frac {e^{\frac {8-6 x+5 x^2-x^3-x^4+e^{4 e^{x^2} x} \left (4-5 x+x^2+x^3\right )}{e^{4 e^{x^2} x} (-4+x)+4 x-x^2}} \left (-32+16 x+14 x^2-8 x^3-11 x^4+2 x^5+e^{8 e^{x^2} x} \left (16-8 x-11 x^2+2 x^3\right )+e^{4 e^{x^2} x} \left (-32 x+16 x^2+22 x^3-4 x^4+e^{x^2} \left (128-64 x+264 x^2-128 x^3+16 x^4\right )\right )\right )}{16 x^2-8 x^3+x^4+e^{8 e^{x^2} x} \left (16-8 x+x^2\right )+e^{4 e^{x^2} x} \left (-32 x+16 x^2-2 x^3\right )} \, dx=e^{\left (x^{2} + 5 \, x + \frac {2 \, e^{\left (4 \, x e^{\left (x^{2}\right )}\right )}}{{\left (x + 4\right )} e^{\left (4 \, x e^{\left (x^{2}\right )}\right )} - 4 \, x - e^{\left (8 \, x e^{\left (x^{2}\right )}\right )}} + \frac {64 \, e^{\left (4 \, x e^{\left (x^{2}\right )}\right )}}{{\left (x - 4\right )} e^{\left (4 \, x e^{\left (x^{2}\right )}\right )} - 4 \, x + 16} - \frac {8}{{\left (x + 4\right )} e^{\left (4 \, x e^{\left (x^{2}\right )}\right )} - 4 \, x - e^{\left (8 \, x e^{\left (x^{2}\right )}\right )}} - \frac {256}{{\left (x - 4\right )} e^{\left (4 \, x e^{\left (x^{2}\right )}\right )} - 4 \, x + 16} + 15\right )} \] Input:
integrate(((2*x^3-11*x^2-8*x+16)*exp(4*exp(x^2)*x)^2+((16*x^4-128*x^3+264* x^2-64*x+128)*exp(x^2)-4*x^4+22*x^3+16*x^2-32*x)*exp(4*exp(x^2)*x)+2*x^5-1 1*x^4-8*x^3+14*x^2+16*x-32)*exp(((x^3+x^2-5*x+4)*exp(4*exp(x^2)*x)-x^4-x^3 +5*x^2-6*x+8)/((-4+x)*exp(4*exp(x^2)*x)-x^2+4*x))/((x^2-8*x+16)*exp(4*exp( x^2)*x)^2+(-2*x^3+16*x^2-32*x)*exp(4*exp(x^2)*x)+x^4-8*x^3+16*x^2),x, algo rithm="maxima")
Output:
e^(x^2 + 5*x + 2*e^(4*x*e^(x^2))/((x + 4)*e^(4*x*e^(x^2)) - 4*x - e^(8*x*e ^(x^2))) + 64*e^(4*x*e^(x^2))/((x - 4)*e^(4*x*e^(x^2)) - 4*x + 16) - 8/((x + 4)*e^(4*x*e^(x^2)) - 4*x - e^(8*x*e^(x^2))) - 256/((x - 4)*e^(4*x*e^(x^ 2)) - 4*x + 16) + 15)
Exception generated. \[ \int \frac {e^{\frac {8-6 x+5 x^2-x^3-x^4+e^{4 e^{x^2} x} \left (4-5 x+x^2+x^3\right )}{e^{4 e^{x^2} x} (-4+x)+4 x-x^2}} \left (-32+16 x+14 x^2-8 x^3-11 x^4+2 x^5+e^{8 e^{x^2} x} \left (16-8 x-11 x^2+2 x^3\right )+e^{4 e^{x^2} x} \left (-32 x+16 x^2+22 x^3-4 x^4+e^{x^2} \left (128-64 x+264 x^2-128 x^3+16 x^4\right )\right )\right )}{16 x^2-8 x^3+x^4+e^{8 e^{x^2} x} \left (16-8 x+x^2\right )+e^{4 e^{x^2} x} \left (-32 x+16 x^2-2 x^3\right )} \, dx=\text {Exception raised: TypeError} \] Input:
integrate(((2*x^3-11*x^2-8*x+16)*exp(4*exp(x^2)*x)^2+((16*x^4-128*x^3+264* x^2-64*x+128)*exp(x^2)-4*x^4+22*x^3+16*x^2-32*x)*exp(4*exp(x^2)*x)+2*x^5-1 1*x^4-8*x^3+14*x^2+16*x-32)*exp(((x^3+x^2-5*x+4)*exp(4*exp(x^2)*x)-x^4-x^3 +5*x^2-6*x+8)/((-4+x)*exp(4*exp(x^2)*x)-x^2+4*x))/((x^2-8*x+16)*exp(4*exp( x^2)*x)^2+(-2*x^3+16*x^2-32*x)*exp(4*exp(x^2)*x)+x^4-8*x^3+16*x^2),x, algo rithm="giac")
Output:
Exception raised: TypeError >> an error occurred running a Giac command:IN PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Unable to divide, perhaps due to ro unding error%%%{4194304,[0,6,35]%%%}+%%%{-257949696,[0,6,34]%%%}+%%%{73945 57952,[0,
Time = 1.70 (sec) , antiderivative size = 354, normalized size of antiderivative = 11.06 \[ \int \frac {e^{\frac {8-6 x+5 x^2-x^3-x^4+e^{4 e^{x^2} x} \left (4-5 x+x^2+x^3\right )}{e^{4 e^{x^2} x} (-4+x)+4 x-x^2}} \left (-32+16 x+14 x^2-8 x^3-11 x^4+2 x^5+e^{8 e^{x^2} x} \left (16-8 x-11 x^2+2 x^3\right )+e^{4 e^{x^2} x} \left (-32 x+16 x^2+22 x^3-4 x^4+e^{x^2} \left (128-64 x+264 x^2-128 x^3+16 x^4\right )\right )\right )}{16 x^2-8 x^3+x^4+e^{8 e^{x^2} x} \left (16-8 x+x^2\right )+e^{4 e^{x^2} x} \left (-32 x+16 x^2-2 x^3\right )} \, dx={\mathrm {e}}^{\frac {x^2\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^{x^2}}}{4\,x-4\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^{x^2}}+x\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^{x^2}}-x^2}}\,{\mathrm {e}}^{\frac {x^3\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^{x^2}}}{4\,x-4\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^{x^2}}+x\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^{x^2}}-x^2}}\,{\mathrm {e}}^{-\frac {6\,x}{4\,x-4\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^{x^2}}+x\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^{x^2}}-x^2}}\,{\mathrm {e}}^{\frac {4\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^{x^2}}}{4\,x-4\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^{x^2}}+x\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^{x^2}}-x^2}}\,{\mathrm {e}}^{-\frac {x^3}{4\,x-4\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^{x^2}}+x\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^{x^2}}-x^2}}\,{\mathrm {e}}^{-\frac {x^4}{4\,x-4\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^{x^2}}+x\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^{x^2}}-x^2}}\,{\mathrm {e}}^{\frac {5\,x^2}{4\,x-4\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^{x^2}}+x\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^{x^2}}-x^2}}\,{\mathrm {e}}^{-\frac {5\,x\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^{x^2}}}{4\,x-4\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^{x^2}}+x\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^{x^2}}-x^2}}\,{\mathrm {e}}^{\frac {8}{4\,x-4\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^{x^2}}+x\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^{x^2}}-x^2}} \] Input:
int((exp(-(6*x - exp(4*x*exp(x^2))*(x^2 - 5*x + x^3 + 4) - 5*x^2 + x^3 + x ^4 - 8)/(4*x + exp(4*x*exp(x^2))*(x - 4) - x^2))*(16*x + exp(4*x*exp(x^2)) *(exp(x^2)*(264*x^2 - 64*x - 128*x^3 + 16*x^4 + 128) - 32*x + 16*x^2 + 22* x^3 - 4*x^4) - exp(8*x*exp(x^2))*(8*x + 11*x^2 - 2*x^3 - 16) + 14*x^2 - 8* x^3 - 11*x^4 + 2*x^5 - 32))/(16*x^2 - exp(4*x*exp(x^2))*(32*x - 16*x^2 + 2 *x^3) - 8*x^3 + x^4 + exp(8*x*exp(x^2))*(x^2 - 8*x + 16)),x)
Output:
exp((x^2*exp(4*x*exp(x^2)))/(4*x - 4*exp(4*x*exp(x^2)) + x*exp(4*x*exp(x^2 )) - x^2))*exp((x^3*exp(4*x*exp(x^2)))/(4*x - 4*exp(4*x*exp(x^2)) + x*exp( 4*x*exp(x^2)) - x^2))*exp(-(6*x)/(4*x - 4*exp(4*x*exp(x^2)) + x*exp(4*x*ex p(x^2)) - x^2))*exp((4*exp(4*x*exp(x^2)))/(4*x - 4*exp(4*x*exp(x^2)) + x*e xp(4*x*exp(x^2)) - x^2))*exp(-x^3/(4*x - 4*exp(4*x*exp(x^2)) + x*exp(4*x*e xp(x^2)) - x^2))*exp(-x^4/(4*x - 4*exp(4*x*exp(x^2)) + x*exp(4*x*exp(x^2)) - x^2))*exp((5*x^2)/(4*x - 4*exp(4*x*exp(x^2)) + x*exp(4*x*exp(x^2)) - x^ 2))*exp(-(5*x*exp(4*x*exp(x^2)))/(4*x - 4*exp(4*x*exp(x^2)) + x*exp(4*x*ex p(x^2)) - x^2))*exp(8/(4*x - 4*exp(4*x*exp(x^2)) + x*exp(4*x*exp(x^2)) - x ^2))
\[ \int \frac {e^{\frac {8-6 x+5 x^2-x^3-x^4+e^{4 e^{x^2} x} \left (4-5 x+x^2+x^3\right )}{e^{4 e^{x^2} x} (-4+x)+4 x-x^2}} \left (-32+16 x+14 x^2-8 x^3-11 x^4+2 x^5+e^{8 e^{x^2} x} \left (16-8 x-11 x^2+2 x^3\right )+e^{4 e^{x^2} x} \left (-32 x+16 x^2+22 x^3-4 x^4+e^{x^2} \left (128-64 x+264 x^2-128 x^3+16 x^4\right )\right )\right )}{16 x^2-8 x^3+x^4+e^{8 e^{x^2} x} \left (16-8 x+x^2\right )+e^{4 e^{x^2} x} \left (-32 x+16 x^2-2 x^3\right )} \, dx=\int \frac {\left (\left (2 x^{3}-11 x^{2}-8 x +16\right ) \left ({\mathrm e}^{4 \,{\mathrm e}^{x^{2}} x}\right )^{2}+\left (\left (16 x^{4}-128 x^{3}+264 x^{2}-64 x +128\right ) {\mathrm e}^{x^{2}}-4 x^{4}+22 x^{3}+16 x^{2}-32 x \right ) {\mathrm e}^{4 \,{\mathrm e}^{x^{2}} x}+2 x^{5}-11 x^{4}-8 x^{3}+14 x^{2}+16 x -32\right ) {\mathrm e}^{\frac {\left (x^{3}+x^{2}-5 x +4\right ) {\mathrm e}^{4 \,{\mathrm e}^{x^{2}} x}-x^{4}-x^{3}+5 x^{2}-6 x +8}{\left (x -4\right ) {\mathrm e}^{4 \,{\mathrm e}^{x^{2}} x}-x^{2}+4 x}}}{\left (x^{2}-8 x +16\right ) \left ({\mathrm e}^{4 \,{\mathrm e}^{x^{2}} x}\right )^{2}+\left (-2 x^{3}+16 x^{2}-32 x \right ) {\mathrm e}^{4 \,{\mathrm e}^{x^{2}} x}+x^{4}-8 x^{3}+16 x^{2}}d x \] Input:
int(((2*x^3-11*x^2-8*x+16)*exp(4*exp(x^2)*x)^2+((16*x^4-128*x^3+264*x^2-64 *x+128)*exp(x^2)-4*x^4+22*x^3+16*x^2-32*x)*exp(4*exp(x^2)*x)+2*x^5-11*x^4- 8*x^3+14*x^2+16*x-32)*exp(((x^3+x^2-5*x+4)*exp(4*exp(x^2)*x)-x^4-x^3+5*x^2 -6*x+8)/((-4+x)*exp(4*exp(x^2)*x)-x^2+4*x))/((x^2-8*x+16)*exp(4*exp(x^2)*x )^2+(-2*x^3+16*x^2-32*x)*exp(4*exp(x^2)*x)+x^4-8*x^3+16*x^2),x)
Output:
int(((2*x^3-11*x^2-8*x+16)*exp(4*exp(x^2)*x)^2+((16*x^4-128*x^3+264*x^2-64 *x+128)*exp(x^2)-4*x^4+22*x^3+16*x^2-32*x)*exp(4*exp(x^2)*x)+2*x^5-11*x^4- 8*x^3+14*x^2+16*x-32)*exp(((x^3+x^2-5*x+4)*exp(4*exp(x^2)*x)-x^4-x^3+5*x^2 -6*x+8)/((-4+x)*exp(4*exp(x^2)*x)-x^2+4*x))/((x^2-8*x+16)*exp(4*exp(x^2)*x )^2+(-2*x^3+16*x^2-32*x)*exp(4*exp(x^2)*x)+x^4-8*x^3+16*x^2),x)