Integrand size = 226, antiderivative size = 42 \[ \int \frac {380 x^4+100 e^{\frac {2 e^{2 x}}{x^2}} x^4-400 x^5+100 x^6+e^x \left (-40 x^2+80 x^3-20 x^4\right )+e^{\frac {e^{2 x}}{x^2}} \left (e^{3 x} (40-40 x)+400 x^4-200 x^5+e^{2 x} \left (-40 x+40 x^2\right )+e^x \left (-20 x^2+20 x^3\right )\right )}{e^{2 x} x^2+x^4-20 x^5+110 x^6+25 e^{\frac {2 e^{2 x}}{x^2}} x^6-100 x^7+25 x^8+e^x \left (-2 x^3+20 x^4-10 x^5\right )+e^{\frac {e^{2 x}}{x^2}} \left (10 e^x x^4-10 x^5+100 x^6-50 x^7\right )} \, dx=\frac {4}{-x+\frac {-e^x+x}{5 \left (2 x+\left (e^{\frac {e^{2 x}}{x^2}}-x\right ) x\right )}} \] Output:
4/(1/5*(x-exp(x))/(2*x+(exp(exp(x)^2/x^2)-x)*x)-x)
Time = 0.10 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.26 \[ \int \frac {380 x^4+100 e^{\frac {2 e^{2 x}}{x^2}} x^4-400 x^5+100 x^6+e^x \left (-40 x^2+80 x^3-20 x^4\right )+e^{\frac {e^{2 x}}{x^2}} \left (e^{3 x} (40-40 x)+400 x^4-200 x^5+e^{2 x} \left (-40 x+40 x^2\right )+e^x \left (-20 x^2+20 x^3\right )\right )}{e^{2 x} x^2+x^4-20 x^5+110 x^6+25 e^{\frac {2 e^{2 x}}{x^2}} x^6-100 x^7+25 x^8+e^x \left (-2 x^3+20 x^4-10 x^5\right )+e^{\frac {e^{2 x}}{x^2}} \left (10 e^x x^4-10 x^5+100 x^6-50 x^7\right )} \, dx=\frac {20 x \left (-2-e^{\frac {e^{2 x}}{x^2}}+x\right )}{e^x+5 e^{\frac {e^{2 x}}{x^2}} x^2+x \left (-1+10 x-5 x^2\right )} \] Input:
Integrate[(380*x^4 + 100*E^((2*E^(2*x))/x^2)*x^4 - 400*x^5 + 100*x^6 + E^x *(-40*x^2 + 80*x^3 - 20*x^4) + E^(E^(2*x)/x^2)*(E^(3*x)*(40 - 40*x) + 400* x^4 - 200*x^5 + E^(2*x)*(-40*x + 40*x^2) + E^x*(-20*x^2 + 20*x^3)))/(E^(2* x)*x^2 + x^4 - 20*x^5 + 110*x^6 + 25*E^((2*E^(2*x))/x^2)*x^6 - 100*x^7 + 2 5*x^8 + E^x*(-2*x^3 + 20*x^4 - 10*x^5) + E^(E^(2*x)/x^2)*(10*E^x*x^4 - 10* x^5 + 100*x^6 - 50*x^7)),x]
Output:
(20*x*(-2 - E^(E^(2*x)/x^2) + x))/(E^x + 5*E^(E^(2*x)/x^2)*x^2 + x*(-1 + 1 0*x - 5*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.
| \(\displaystyle \int \frac {100 x^6-400 x^5+380 x^4+100 e^{\frac {2 e^{2 x}}{x^2}} x^4+e^x \left (-20 x^4+80 x^3-40 x^2\right )+e^{\frac {e^{2 x}}{x^2}} \left (-200 x^5+400 x^4+e^{2 x} \left (40 x^2-40 x\right )+e^x \left (20 x^3-20 x^2\right )+e^{3 x} (40-40 x)\right )}{25 x^8-100 x^7+110 x^6-20 x^5+x^4+e^{2 x} x^2+25 e^{\frac {2 e^{2 x}}{x^2}} x^6+e^x \left (-10 x^5+20 x^4-2 x^3\right )+e^{\frac {e^{2 x}}{x^2}} \left (-50 x^7+100 x^6-10 x^5+10 e^x x^4\right )} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {100 x^6-400 x^5+380 x^4+100 e^{\frac {2 e^{2 x}}{x^2}} x^4+e^x \left (-20 x^4+80 x^3-40 x^2\right )+e^{\frac {e^{2 x}}{x^2}} \left (-200 x^5+400 x^4+e^{2 x} \left (40 x^2-40 x\right )+e^x \left (20 x^3-20 x^2\right )+e^{3 x} (40-40 x)\right )}{x^2 \left (-5 x^3+5 e^{\frac {e^{2 x}}{x^2}} x^2+10 x^2-x+e^x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {40 e^{\frac {e^{2 x}}{x^2}} \left (-10 x^2+10 e^{\frac {e^{2 x}}{x^2}} x+20 x-1\right ) (x-1)}{x}-\frac {40 e^{\frac {e^{2 x}}{x^2}+x} (x-1)}{x^2}-\frac {20 \left (-720 e^{\frac {e^{2 x}}{x^2}} x^2-640 e^{\frac {2 e^{2 x}}{x^2}} x^2-150 e^{\frac {3 e^{2 x}}{x^2}} x^2+x^2+81 e^{\frac {e^{2 x}}{x^2}} x+40 e^{\frac {2 e^{2 x}}{x^2}} x-e^{\frac {e^{2 x}}{x^2}}+150 e^{\frac {e^{2 x}}{x^2}} x^5-750 e^{\frac {e^{2 x}}{x^2}} x^4-300 e^{\frac {2 e^{2 x}}{x^2}} x^4+1240 e^{\frac {e^{2 x}}{x^2}} x^3+900 e^{\frac {2 e^{2 x}}{x^2}} x^3+150 e^{\frac {3 e^{2 x}}{x^2}} x^3-4 x+2\right )}{-5 x^3+5 e^{\frac {e^{2 x}}{x^2}} x^2+10 x^2-x+e^x}-\frac {20 x \left (5 x^4-35 x^3-385 e^{\frac {e^{2 x}}{x^2}} x^2-405 e^{\frac {2 e^{2 x}}{x^2}} x^2-100 e^{\frac {3 e^{2 x}}{x^2}} x^2+71 x^2-21 e^{\frac {e^{2 x}}{x^2}} x+e^{\frac {e^{2 x}}{x^2}}+250 e^{\frac {e^{2 x}}{x^2}} x^7-1750 e^{\frac {e^{2 x}}{x^2}} x^6-750 e^{\frac {2 e^{2 x}}{x^2}} x^6+4600 e^{\frac {e^{2 x}}{x^2}} x^5+3750 e^{\frac {2 e^{2 x}}{x^2}} x^5+750 e^{\frac {3 e^{2 x}}{x^2}} x^5-5500 e^{\frac {e^{2 x}}{x^2}} x^4-6200 e^{\frac {2 e^{2 x}}{x^2}} x^4-2250 e^{\frac {3 e^{2 x}}{x^2}} x^4-250 e^{\frac {4 e^{2 x}}{x^2}} x^4+2800 e^{\frac {e^{2 x}}{x^2}} x^3+3600 e^{\frac {2 e^{2 x}}{x^2}} x^3+1600 e^{\frac {3 e^{2 x}}{x^2}} x^3+250 e^{\frac {4 e^{2 x}}{x^2}} x^3-43 x+2\right )}{\left (5 x^3-5 e^{\frac {e^{2 x}}{x^2}} x^2-10 x^2+x-e^x\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {20 \left (e^{\frac {e^{2 x}}{x^2}+x} (x-1) x^2-e^x \left (x^2-4 x+2\right ) x^2+2 e^{\frac {e^{2 x}}{x^2}+2 x} (x-1) x-2 e^{\frac {e^{2 x}}{x^2}+3 x} (x-1)+5 e^{\frac {2 e^{2 x}}{x^2}} x^4-10 e^{\frac {e^{2 x}}{x^2}} (x-2) x^4+\left (5 x^2-20 x+19\right ) x^4\right )}{x^2 \left (5 e^{\frac {e^{2 x}}{x^2}} x^2+\left (-5 x^2+10 x-1\right ) x+e^x\right )^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 20 \int \frac {5 e^{\frac {2 e^{2 x}}{x^2}} x^4+10 e^{\frac {e^{2 x}}{x^2}} (2-x) x^4+\left (5 x^2-20 x+19\right ) x^4-e^{x+\frac {e^{2 x}}{x^2}} (1-x) x^2-e^x \left (x^2-4 x+2\right ) x^2-2 e^{2 x+\frac {e^{2 x}}{x^2}} (1-x) x+2 e^{3 x+\frac {e^{2 x}}{x^2}} (1-x)}{x^2 \left (5 e^{\frac {e^{2 x}}{x^2}} x^2-\left (5 x^2-10 x+1\right ) x+e^x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 20 \int \left (\frac {2 e^{\frac {e^{2 x}}{x^2}} \left (-10 x^2+10 e^{\frac {e^{2 x}}{x^2}} x+20 x-1\right ) (x-1)}{x}-\frac {2 e^{x+\frac {e^{2 x}}{x^2}} (x-1)}{x^2}-\frac {150 e^{\frac {e^{2 x}}{x^2}} x^5-750 e^{\frac {e^{2 x}}{x^2}} x^4-300 e^{\frac {2 e^{2 x}}{x^2}} x^4+1240 e^{\frac {e^{2 x}}{x^2}} x^3+900 e^{\frac {2 e^{2 x}}{x^2}} x^3+150 e^{\frac {3 e^{2 x}}{x^2}} x^3-720 e^{\frac {e^{2 x}}{x^2}} x^2-640 e^{\frac {2 e^{2 x}}{x^2}} x^2-150 e^{\frac {3 e^{2 x}}{x^2}} x^2+x^2+81 e^{\frac {e^{2 x}}{x^2}} x+40 e^{\frac {2 e^{2 x}}{x^2}} x-4 x-e^{\frac {e^{2 x}}{x^2}}+2}{-5 x^3+5 e^{\frac {e^{2 x}}{x^2}} x^2+10 x^2-x+e^x}-\frac {x \left (250 e^{\frac {e^{2 x}}{x^2}} x^7-1750 e^{\frac {e^{2 x}}{x^2}} x^6-750 e^{\frac {2 e^{2 x}}{x^2}} x^6+4600 e^{\frac {e^{2 x}}{x^2}} x^5+3750 e^{\frac {2 e^{2 x}}{x^2}} x^5+750 e^{\frac {3 e^{2 x}}{x^2}} x^5-5500 e^{\frac {e^{2 x}}{x^2}} x^4-6200 e^{\frac {2 e^{2 x}}{x^2}} x^4-2250 e^{\frac {3 e^{2 x}}{x^2}} x^4-250 e^{\frac {4 e^{2 x}}{x^2}} x^4+5 x^4+2800 e^{\frac {e^{2 x}}{x^2}} x^3+3600 e^{\frac {2 e^{2 x}}{x^2}} x^3+1600 e^{\frac {3 e^{2 x}}{x^2}} x^3+250 e^{\frac {4 e^{2 x}}{x^2}} x^3-35 x^3-385 e^{\frac {e^{2 x}}{x^2}} x^2-405 e^{\frac {2 e^{2 x}}{x^2}} x^2-100 e^{\frac {3 e^{2 x}}{x^2}} x^2+71 x^2-21 e^{\frac {e^{2 x}}{x^2}} x-43 x+e^{\frac {e^{2 x}}{x^2}}+2\right )}{\left (5 x^3-5 e^{\frac {e^{2 x}}{x^2}} x^2-10 x^2+x-e^x\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 20 \int \frac {5 e^{\frac {2 e^{2 x}}{x^2}} x^4-10 e^{\frac {e^{2 x}}{x^2}} (x-2) x^4+\left (5 x^2-20 x+19\right ) x^4+e^{x+\frac {e^{2 x}}{x^2}} (x-1) x^2-e^x \left (x^2-4 x+2\right ) x^2+2 e^{2 x+\frac {e^{2 x}}{x^2}} (x-1) x-2 e^{3 x+\frac {e^{2 x}}{x^2}} (x-1)}{x^2 \left (5 e^{\frac {e^{2 x}}{x^2}} x^2+\left (-5 x^2+10 x-1\right ) x+e^x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 20 \int \left (\frac {2 e^{\frac {e^{2 x}}{x^2}} \left (-10 x^2+10 e^{\frac {e^{2 x}}{x^2}} x+20 x-1\right ) (x-1)}{x}-\frac {2 e^{x+\frac {e^{2 x}}{x^2}} (x-1)}{x^2}-\frac {150 e^{\frac {e^{2 x}}{x^2}} x^5-750 e^{\frac {e^{2 x}}{x^2}} x^4-300 e^{\frac {2 e^{2 x}}{x^2}} x^4+1240 e^{\frac {e^{2 x}}{x^2}} x^3+900 e^{\frac {2 e^{2 x}}{x^2}} x^3+150 e^{\frac {3 e^{2 x}}{x^2}} x^3-720 e^{\frac {e^{2 x}}{x^2}} x^2-640 e^{\frac {2 e^{2 x}}{x^2}} x^2-150 e^{\frac {3 e^{2 x}}{x^2}} x^2+x^2+81 e^{\frac {e^{2 x}}{x^2}} x+40 e^{\frac {2 e^{2 x}}{x^2}} x-4 x-e^{\frac {e^{2 x}}{x^2}}+2}{-5 x^3+5 e^{\frac {e^{2 x}}{x^2}} x^2+10 x^2-x+e^x}-\frac {x \left (250 e^{\frac {e^{2 x}}{x^2}} x^7-1750 e^{\frac {e^{2 x}}{x^2}} x^6-750 e^{\frac {2 e^{2 x}}{x^2}} x^6+4600 e^{\frac {e^{2 x}}{x^2}} x^5+3750 e^{\frac {2 e^{2 x}}{x^2}} x^5+750 e^{\frac {3 e^{2 x}}{x^2}} x^5-5500 e^{\frac {e^{2 x}}{x^2}} x^4-6200 e^{\frac {2 e^{2 x}}{x^2}} x^4-2250 e^{\frac {3 e^{2 x}}{x^2}} x^4-250 e^{\frac {4 e^{2 x}}{x^2}} x^4+5 x^4+2800 e^{\frac {e^{2 x}}{x^2}} x^3+3600 e^{\frac {2 e^{2 x}}{x^2}} x^3+1600 e^{\frac {3 e^{2 x}}{x^2}} x^3+250 e^{\frac {4 e^{2 x}}{x^2}} x^3-35 x^3-385 e^{\frac {e^{2 x}}{x^2}} x^2-405 e^{\frac {2 e^{2 x}}{x^2}} x^2-100 e^{\frac {3 e^{2 x}}{x^2}} x^2+71 x^2-21 e^{\frac {e^{2 x}}{x^2}} x-43 x+e^{\frac {e^{2 x}}{x^2}}+2\right )}{\left (5 x^3-5 e^{\frac {e^{2 x}}{x^2}} x^2-10 x^2+x-e^x\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 20 \int \frac {5 e^{\frac {2 e^{2 x}}{x^2}} x^4-10 e^{\frac {e^{2 x}}{x^2}} (x-2) x^4+\left (5 x^2-20 x+19\right ) x^4+e^{x+\frac {e^{2 x}}{x^2}} (x-1) x^2-e^x \left (x^2-4 x+2\right ) x^2+2 e^{2 x+\frac {e^{2 x}}{x^2}} (x-1) x-2 e^{3 x+\frac {e^{2 x}}{x^2}} (x-1)}{x^2 \left (5 e^{\frac {e^{2 x}}{x^2}} x^2+\left (-5 x^2+10 x-1\right ) x+e^x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 20 \int \left (\frac {2 e^{\frac {e^{2 x}}{x^2}} \left (-10 x^2+10 e^{\frac {e^{2 x}}{x^2}} x+20 x-1\right ) (x-1)}{x}-\frac {2 e^{x+\frac {e^{2 x}}{x^2}} (x-1)}{x^2}-\frac {150 e^{\frac {e^{2 x}}{x^2}} x^5-750 e^{\frac {e^{2 x}}{x^2}} x^4-300 e^{\frac {2 e^{2 x}}{x^2}} x^4+1240 e^{\frac {e^{2 x}}{x^2}} x^3+900 e^{\frac {2 e^{2 x}}{x^2}} x^3+150 e^{\frac {3 e^{2 x}}{x^2}} x^3-720 e^{\frac {e^{2 x}}{x^2}} x^2-640 e^{\frac {2 e^{2 x}}{x^2}} x^2-150 e^{\frac {3 e^{2 x}}{x^2}} x^2+x^2+81 e^{\frac {e^{2 x}}{x^2}} x+40 e^{\frac {2 e^{2 x}}{x^2}} x-4 x-e^{\frac {e^{2 x}}{x^2}}+2}{-5 x^3+5 e^{\frac {e^{2 x}}{x^2}} x^2+10 x^2-x+e^x}-\frac {x \left (250 e^{\frac {e^{2 x}}{x^2}} x^7-1750 e^{\frac {e^{2 x}}{x^2}} x^6-750 e^{\frac {2 e^{2 x}}{x^2}} x^6+4600 e^{\frac {e^{2 x}}{x^2}} x^5+3750 e^{\frac {2 e^{2 x}}{x^2}} x^5+750 e^{\frac {3 e^{2 x}}{x^2}} x^5-5500 e^{\frac {e^{2 x}}{x^2}} x^4-6200 e^{\frac {2 e^{2 x}}{x^2}} x^4-2250 e^{\frac {3 e^{2 x}}{x^2}} x^4-250 e^{\frac {4 e^{2 x}}{x^2}} x^4+5 x^4+2800 e^{\frac {e^{2 x}}{x^2}} x^3+3600 e^{\frac {2 e^{2 x}}{x^2}} x^3+1600 e^{\frac {3 e^{2 x}}{x^2}} x^3+250 e^{\frac {4 e^{2 x}}{x^2}} x^3-35 x^3-385 e^{\frac {e^{2 x}}{x^2}} x^2-405 e^{\frac {2 e^{2 x}}{x^2}} x^2-100 e^{\frac {3 e^{2 x}}{x^2}} x^2+71 x^2-21 e^{\frac {e^{2 x}}{x^2}} x-43 x+e^{\frac {e^{2 x}}{x^2}}+2\right )}{\left (5 x^3-5 e^{\frac {e^{2 x}}{x^2}} x^2-10 x^2+x-e^x\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 20 \int \frac {5 e^{\frac {2 e^{2 x}}{x^2}} x^4-10 e^{\frac {e^{2 x}}{x^2}} (x-2) x^4+\left (5 x^2-20 x+19\right ) x^4+e^{x+\frac {e^{2 x}}{x^2}} (x-1) x^2-e^x \left (x^2-4 x+2\right ) x^2+2 e^{2 x+\frac {e^{2 x}}{x^2}} (x-1) x-2 e^{3 x+\frac {e^{2 x}}{x^2}} (x-1)}{x^2 \left (5 e^{\frac {e^{2 x}}{x^2}} x^2+\left (-5 x^2+10 x-1\right ) x+e^x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 20 \int \left (\frac {2 e^{\frac {e^{2 x}}{x^2}} \left (-10 x^2+10 e^{\frac {e^{2 x}}{x^2}} x+20 x-1\right ) (x-1)}{x}-\frac {2 e^{x+\frac {e^{2 x}}{x^2}} (x-1)}{x^2}-\frac {150 e^{\frac {e^{2 x}}{x^2}} x^5-750 e^{\frac {e^{2 x}}{x^2}} x^4-300 e^{\frac {2 e^{2 x}}{x^2}} x^4+1240 e^{\frac {e^{2 x}}{x^2}} x^3+900 e^{\frac {2 e^{2 x}}{x^2}} x^3+150 e^{\frac {3 e^{2 x}}{x^2}} x^3-720 e^{\frac {e^{2 x}}{x^2}} x^2-640 e^{\frac {2 e^{2 x}}{x^2}} x^2-150 e^{\frac {3 e^{2 x}}{x^2}} x^2+x^2+81 e^{\frac {e^{2 x}}{x^2}} x+40 e^{\frac {2 e^{2 x}}{x^2}} x-4 x-e^{\frac {e^{2 x}}{x^2}}+2}{-5 x^3+5 e^{\frac {e^{2 x}}{x^2}} x^2+10 x^2-x+e^x}-\frac {x \left (250 e^{\frac {e^{2 x}}{x^2}} x^7-1750 e^{\frac {e^{2 x}}{x^2}} x^6-750 e^{\frac {2 e^{2 x}}{x^2}} x^6+4600 e^{\frac {e^{2 x}}{x^2}} x^5+3750 e^{\frac {2 e^{2 x}}{x^2}} x^5+750 e^{\frac {3 e^{2 x}}{x^2}} x^5-5500 e^{\frac {e^{2 x}}{x^2}} x^4-6200 e^{\frac {2 e^{2 x}}{x^2}} x^4-2250 e^{\frac {3 e^{2 x}}{x^2}} x^4-250 e^{\frac {4 e^{2 x}}{x^2}} x^4+5 x^4+2800 e^{\frac {e^{2 x}}{x^2}} x^3+3600 e^{\frac {2 e^{2 x}}{x^2}} x^3+1600 e^{\frac {3 e^{2 x}}{x^2}} x^3+250 e^{\frac {4 e^{2 x}}{x^2}} x^3-35 x^3-385 e^{\frac {e^{2 x}}{x^2}} x^2-405 e^{\frac {2 e^{2 x}}{x^2}} x^2-100 e^{\frac {3 e^{2 x}}{x^2}} x^2+71 x^2-21 e^{\frac {e^{2 x}}{x^2}} x-43 x+e^{\frac {e^{2 x}}{x^2}}+2\right )}{\left (5 x^3-5 e^{\frac {e^{2 x}}{x^2}} x^2-10 x^2+x-e^x\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 20 \int \frac {5 e^{\frac {2 e^{2 x}}{x^2}} x^4-10 e^{\frac {e^{2 x}}{x^2}} (x-2) x^4+\left (5 x^2-20 x+19\right ) x^4+e^{x+\frac {e^{2 x}}{x^2}} (x-1) x^2-e^x \left (x^2-4 x+2\right ) x^2+2 e^{2 x+\frac {e^{2 x}}{x^2}} (x-1) x-2 e^{3 x+\frac {e^{2 x}}{x^2}} (x-1)}{x^2 \left (5 e^{\frac {e^{2 x}}{x^2}} x^2+\left (-5 x^2+10 x-1\right ) x+e^x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 20 \int \left (\frac {2 e^{\frac {e^{2 x}}{x^2}} \left (-10 x^2+10 e^{\frac {e^{2 x}}{x^2}} x+20 x-1\right ) (x-1)}{x}-\frac {2 e^{x+\frac {e^{2 x}}{x^2}} (x-1)}{x^2}-\frac {150 e^{\frac {e^{2 x}}{x^2}} x^5-750 e^{\frac {e^{2 x}}{x^2}} x^4-300 e^{\frac {2 e^{2 x}}{x^2}} x^4+1240 e^{\frac {e^{2 x}}{x^2}} x^3+900 e^{\frac {2 e^{2 x}}{x^2}} x^3+150 e^{\frac {3 e^{2 x}}{x^2}} x^3-720 e^{\frac {e^{2 x}}{x^2}} x^2-640 e^{\frac {2 e^{2 x}}{x^2}} x^2-150 e^{\frac {3 e^{2 x}}{x^2}} x^2+x^2+81 e^{\frac {e^{2 x}}{x^2}} x+40 e^{\frac {2 e^{2 x}}{x^2}} x-4 x-e^{\frac {e^{2 x}}{x^2}}+2}{-5 x^3+5 e^{\frac {e^{2 x}}{x^2}} x^2+10 x^2-x+e^x}-\frac {x \left (250 e^{\frac {e^{2 x}}{x^2}} x^7-1750 e^{\frac {e^{2 x}}{x^2}} x^6-750 e^{\frac {2 e^{2 x}}{x^2}} x^6+4600 e^{\frac {e^{2 x}}{x^2}} x^5+3750 e^{\frac {2 e^{2 x}}{x^2}} x^5+750 e^{\frac {3 e^{2 x}}{x^2}} x^5-5500 e^{\frac {e^{2 x}}{x^2}} x^4-6200 e^{\frac {2 e^{2 x}}{x^2}} x^4-2250 e^{\frac {3 e^{2 x}}{x^2}} x^4-250 e^{\frac {4 e^{2 x}}{x^2}} x^4+5 x^4+2800 e^{\frac {e^{2 x}}{x^2}} x^3+3600 e^{\frac {2 e^{2 x}}{x^2}} x^3+1600 e^{\frac {3 e^{2 x}}{x^2}} x^3+250 e^{\frac {4 e^{2 x}}{x^2}} x^3-35 x^3-385 e^{\frac {e^{2 x}}{x^2}} x^2-405 e^{\frac {2 e^{2 x}}{x^2}} x^2-100 e^{\frac {3 e^{2 x}}{x^2}} x^2+71 x^2-21 e^{\frac {e^{2 x}}{x^2}} x-43 x+e^{\frac {e^{2 x}}{x^2}}+2\right )}{\left (5 x^3-5 e^{\frac {e^{2 x}}{x^2}} x^2-10 x^2+x-e^x\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 20 \int \frac {5 e^{\frac {2 e^{2 x}}{x^2}} x^4-10 e^{\frac {e^{2 x}}{x^2}} (x-2) x^4+\left (5 x^2-20 x+19\right ) x^4+e^{x+\frac {e^{2 x}}{x^2}} (x-1) x^2-e^x \left (x^2-4 x+2\right ) x^2+2 e^{2 x+\frac {e^{2 x}}{x^2}} (x-1) x-2 e^{3 x+\frac {e^{2 x}}{x^2}} (x-1)}{x^2 \left (5 e^{\frac {e^{2 x}}{x^2}} x^2+\left (-5 x^2+10 x-1\right ) x+e^x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 20 \int \left (\frac {2 e^{\frac {e^{2 x}}{x^2}} \left (-10 x^2+10 e^{\frac {e^{2 x}}{x^2}} x+20 x-1\right ) (x-1)}{x}-\frac {2 e^{x+\frac {e^{2 x}}{x^2}} (x-1)}{x^2}-\frac {150 e^{\frac {e^{2 x}}{x^2}} x^5-750 e^{\frac {e^{2 x}}{x^2}} x^4-300 e^{\frac {2 e^{2 x}}{x^2}} x^4+1240 e^{\frac {e^{2 x}}{x^2}} x^3+900 e^{\frac {2 e^{2 x}}{x^2}} x^3+150 e^{\frac {3 e^{2 x}}{x^2}} x^3-720 e^{\frac {e^{2 x}}{x^2}} x^2-640 e^{\frac {2 e^{2 x}}{x^2}} x^2-150 e^{\frac {3 e^{2 x}}{x^2}} x^2+x^2+81 e^{\frac {e^{2 x}}{x^2}} x+40 e^{\frac {2 e^{2 x}}{x^2}} x-4 x-e^{\frac {e^{2 x}}{x^2}}+2}{-5 x^3+5 e^{\frac {e^{2 x}}{x^2}} x^2+10 x^2-x+e^x}-\frac {x \left (250 e^{\frac {e^{2 x}}{x^2}} x^7-1750 e^{\frac {e^{2 x}}{x^2}} x^6-750 e^{\frac {2 e^{2 x}}{x^2}} x^6+4600 e^{\frac {e^{2 x}}{x^2}} x^5+3750 e^{\frac {2 e^{2 x}}{x^2}} x^5+750 e^{\frac {3 e^{2 x}}{x^2}} x^5-5500 e^{\frac {e^{2 x}}{x^2}} x^4-6200 e^{\frac {2 e^{2 x}}{x^2}} x^4-2250 e^{\frac {3 e^{2 x}}{x^2}} x^4-250 e^{\frac {4 e^{2 x}}{x^2}} x^4+5 x^4+2800 e^{\frac {e^{2 x}}{x^2}} x^3+3600 e^{\frac {2 e^{2 x}}{x^2}} x^3+1600 e^{\frac {3 e^{2 x}}{x^2}} x^3+250 e^{\frac {4 e^{2 x}}{x^2}} x^3-35 x^3-385 e^{\frac {e^{2 x}}{x^2}} x^2-405 e^{\frac {2 e^{2 x}}{x^2}} x^2-100 e^{\frac {3 e^{2 x}}{x^2}} x^2+71 x^2-21 e^{\frac {e^{2 x}}{x^2}} x-43 x+e^{\frac {e^{2 x}}{x^2}}+2\right )}{\left (5 x^3-5 e^{\frac {e^{2 x}}{x^2}} x^2-10 x^2+x-e^x\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 20 \int \frac {5 e^{\frac {2 e^{2 x}}{x^2}} x^4-10 e^{\frac {e^{2 x}}{x^2}} (x-2) x^4+\left (5 x^2-20 x+19\right ) x^4+e^{x+\frac {e^{2 x}}{x^2}} (x-1) x^2-e^x \left (x^2-4 x+2\right ) x^2+2 e^{2 x+\frac {e^{2 x}}{x^2}} (x-1) x-2 e^{3 x+\frac {e^{2 x}}{x^2}} (x-1)}{x^2 \left (5 e^{\frac {e^{2 x}}{x^2}} x^2+\left (-5 x^2+10 x-1\right ) x+e^x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 20 \int \left (\frac {2 e^{\frac {e^{2 x}}{x^2}} \left (-10 x^2+10 e^{\frac {e^{2 x}}{x^2}} x+20 x-1\right ) (x-1)}{x}-\frac {2 e^{x+\frac {e^{2 x}}{x^2}} (x-1)}{x^2}-\frac {150 e^{\frac {e^{2 x}}{x^2}} x^5-750 e^{\frac {e^{2 x}}{x^2}} x^4-300 e^{\frac {2 e^{2 x}}{x^2}} x^4+1240 e^{\frac {e^{2 x}}{x^2}} x^3+900 e^{\frac {2 e^{2 x}}{x^2}} x^3+150 e^{\frac {3 e^{2 x}}{x^2}} x^3-720 e^{\frac {e^{2 x}}{x^2}} x^2-640 e^{\frac {2 e^{2 x}}{x^2}} x^2-150 e^{\frac {3 e^{2 x}}{x^2}} x^2+x^2+81 e^{\frac {e^{2 x}}{x^2}} x+40 e^{\frac {2 e^{2 x}}{x^2}} x-4 x-e^{\frac {e^{2 x}}{x^2}}+2}{-5 x^3+5 e^{\frac {e^{2 x}}{x^2}} x^2+10 x^2-x+e^x}-\frac {x \left (250 e^{\frac {e^{2 x}}{x^2}} x^7-1750 e^{\frac {e^{2 x}}{x^2}} x^6-750 e^{\frac {2 e^{2 x}}{x^2}} x^6+4600 e^{\frac {e^{2 x}}{x^2}} x^5+3750 e^{\frac {2 e^{2 x}}{x^2}} x^5+750 e^{\frac {3 e^{2 x}}{x^2}} x^5-5500 e^{\frac {e^{2 x}}{x^2}} x^4-6200 e^{\frac {2 e^{2 x}}{x^2}} x^4-2250 e^{\frac {3 e^{2 x}}{x^2}} x^4-250 e^{\frac {4 e^{2 x}}{x^2}} x^4+5 x^4+2800 e^{\frac {e^{2 x}}{x^2}} x^3+3600 e^{\frac {2 e^{2 x}}{x^2}} x^3+1600 e^{\frac {3 e^{2 x}}{x^2}} x^3+250 e^{\frac {4 e^{2 x}}{x^2}} x^3-35 x^3-385 e^{\frac {e^{2 x}}{x^2}} x^2-405 e^{\frac {2 e^{2 x}}{x^2}} x^2-100 e^{\frac {3 e^{2 x}}{x^2}} x^2+71 x^2-21 e^{\frac {e^{2 x}}{x^2}} x-43 x+e^{\frac {e^{2 x}}{x^2}}+2\right )}{\left (5 x^3-5 e^{\frac {e^{2 x}}{x^2}} x^2-10 x^2+x-e^x\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 20 \int \frac {5 e^{\frac {2 e^{2 x}}{x^2}} x^4-10 e^{\frac {e^{2 x}}{x^2}} (x-2) x^4+\left (5 x^2-20 x+19\right ) x^4+e^{x+\frac {e^{2 x}}{x^2}} (x-1) x^2-e^x \left (x^2-4 x+2\right ) x^2+2 e^{2 x+\frac {e^{2 x}}{x^2}} (x-1) x-2 e^{3 x+\frac {e^{2 x}}{x^2}} (x-1)}{x^2 \left (5 e^{\frac {e^{2 x}}{x^2}} x^2+\left (-5 x^2+10 x-1\right ) x+e^x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 20 \int \left (\frac {2 e^{\frac {e^{2 x}}{x^2}} \left (-10 x^2+10 e^{\frac {e^{2 x}}{x^2}} x+20 x-1\right ) (x-1)}{x}-\frac {2 e^{x+\frac {e^{2 x}}{x^2}} (x-1)}{x^2}-\frac {150 e^{\frac {e^{2 x}}{x^2}} x^5-750 e^{\frac {e^{2 x}}{x^2}} x^4-300 e^{\frac {2 e^{2 x}}{x^2}} x^4+1240 e^{\frac {e^{2 x}}{x^2}} x^3+900 e^{\frac {2 e^{2 x}}{x^2}} x^3+150 e^{\frac {3 e^{2 x}}{x^2}} x^3-720 e^{\frac {e^{2 x}}{x^2}} x^2-640 e^{\frac {2 e^{2 x}}{x^2}} x^2-150 e^{\frac {3 e^{2 x}}{x^2}} x^2+x^2+81 e^{\frac {e^{2 x}}{x^2}} x+40 e^{\frac {2 e^{2 x}}{x^2}} x-4 x-e^{\frac {e^{2 x}}{x^2}}+2}{-5 x^3+5 e^{\frac {e^{2 x}}{x^2}} x^2+10 x^2-x+e^x}-\frac {x \left (250 e^{\frac {e^{2 x}}{x^2}} x^7-1750 e^{\frac {e^{2 x}}{x^2}} x^6-750 e^{\frac {2 e^{2 x}}{x^2}} x^6+4600 e^{\frac {e^{2 x}}{x^2}} x^5+3750 e^{\frac {2 e^{2 x}}{x^2}} x^5+750 e^{\frac {3 e^{2 x}}{x^2}} x^5-5500 e^{\frac {e^{2 x}}{x^2}} x^4-6200 e^{\frac {2 e^{2 x}}{x^2}} x^4-2250 e^{\frac {3 e^{2 x}}{x^2}} x^4-250 e^{\frac {4 e^{2 x}}{x^2}} x^4+5 x^4+2800 e^{\frac {e^{2 x}}{x^2}} x^3+3600 e^{\frac {2 e^{2 x}}{x^2}} x^3+1600 e^{\frac {3 e^{2 x}}{x^2}} x^3+250 e^{\frac {4 e^{2 x}}{x^2}} x^3-35 x^3-385 e^{\frac {e^{2 x}}{x^2}} x^2-405 e^{\frac {2 e^{2 x}}{x^2}} x^2-100 e^{\frac {3 e^{2 x}}{x^2}} x^2+71 x^2-21 e^{\frac {e^{2 x}}{x^2}} x-43 x+e^{\frac {e^{2 x}}{x^2}}+2\right )}{\left (5 x^3-5 e^{\frac {e^{2 x}}{x^2}} x^2-10 x^2+x-e^x\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 20 \int \frac {5 e^{\frac {2 e^{2 x}}{x^2}} x^4-10 e^{\frac {e^{2 x}}{x^2}} (x-2) x^4+\left (5 x^2-20 x+19\right ) x^4+e^{x+\frac {e^{2 x}}{x^2}} (x-1) x^2-e^x \left (x^2-4 x+2\right ) x^2+2 e^{2 x+\frac {e^{2 x}}{x^2}} (x-1) x-2 e^{3 x+\frac {e^{2 x}}{x^2}} (x-1)}{x^2 \left (5 e^{\frac {e^{2 x}}{x^2}} x^2+\left (-5 x^2+10 x-1\right ) x+e^x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 20 \int \left (\frac {2 e^{\frac {e^{2 x}}{x^2}} \left (-10 x^2+10 e^{\frac {e^{2 x}}{x^2}} x+20 x-1\right ) (x-1)}{x}-\frac {2 e^{x+\frac {e^{2 x}}{x^2}} (x-1)}{x^2}-\frac {150 e^{\frac {e^{2 x}}{x^2}} x^5-750 e^{\frac {e^{2 x}}{x^2}} x^4-300 e^{\frac {2 e^{2 x}}{x^2}} x^4+1240 e^{\frac {e^{2 x}}{x^2}} x^3+900 e^{\frac {2 e^{2 x}}{x^2}} x^3+150 e^{\frac {3 e^{2 x}}{x^2}} x^3-720 e^{\frac {e^{2 x}}{x^2}} x^2-640 e^{\frac {2 e^{2 x}}{x^2}} x^2-150 e^{\frac {3 e^{2 x}}{x^2}} x^2+x^2+81 e^{\frac {e^{2 x}}{x^2}} x+40 e^{\frac {2 e^{2 x}}{x^2}} x-4 x-e^{\frac {e^{2 x}}{x^2}}+2}{-5 x^3+5 e^{\frac {e^{2 x}}{x^2}} x^2+10 x^2-x+e^x}-\frac {x \left (250 e^{\frac {e^{2 x}}{x^2}} x^7-1750 e^{\frac {e^{2 x}}{x^2}} x^6-750 e^{\frac {2 e^{2 x}}{x^2}} x^6+4600 e^{\frac {e^{2 x}}{x^2}} x^5+3750 e^{\frac {2 e^{2 x}}{x^2}} x^5+750 e^{\frac {3 e^{2 x}}{x^2}} x^5-5500 e^{\frac {e^{2 x}}{x^2}} x^4-6200 e^{\frac {2 e^{2 x}}{x^2}} x^4-2250 e^{\frac {3 e^{2 x}}{x^2}} x^4-250 e^{\frac {4 e^{2 x}}{x^2}} x^4+5 x^4+2800 e^{\frac {e^{2 x}}{x^2}} x^3+3600 e^{\frac {2 e^{2 x}}{x^2}} x^3+1600 e^{\frac {3 e^{2 x}}{x^2}} x^3+250 e^{\frac {4 e^{2 x}}{x^2}} x^3-35 x^3-385 e^{\frac {e^{2 x}}{x^2}} x^2-405 e^{\frac {2 e^{2 x}}{x^2}} x^2-100 e^{\frac {3 e^{2 x}}{x^2}} x^2+71 x^2-21 e^{\frac {e^{2 x}}{x^2}} x-43 x+e^{\frac {e^{2 x}}{x^2}}+2\right )}{\left (5 x^3-5 e^{\frac {e^{2 x}}{x^2}} x^2-10 x^2+x-e^x\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 20 \int \frac {5 e^{\frac {2 e^{2 x}}{x^2}} x^4-10 e^{\frac {e^{2 x}}{x^2}} (x-2) x^4+\left (5 x^2-20 x+19\right ) x^4+e^{x+\frac {e^{2 x}}{x^2}} (x-1) x^2-e^x \left (x^2-4 x+2\right ) x^2+2 e^{2 x+\frac {e^{2 x}}{x^2}} (x-1) x-2 e^{3 x+\frac {e^{2 x}}{x^2}} (x-1)}{x^2 \left (5 e^{\frac {e^{2 x}}{x^2}} x^2+\left (-5 x^2+10 x-1\right ) x+e^x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 20 \int \left (\frac {2 e^{\frac {e^{2 x}}{x^2}} \left (-10 x^2+10 e^{\frac {e^{2 x}}{x^2}} x+20 x-1\right ) (x-1)}{x}-\frac {2 e^{x+\frac {e^{2 x}}{x^2}} (x-1)}{x^2}-\frac {150 e^{\frac {e^{2 x}}{x^2}} x^5-750 e^{\frac {e^{2 x}}{x^2}} x^4-300 e^{\frac {2 e^{2 x}}{x^2}} x^4+1240 e^{\frac {e^{2 x}}{x^2}} x^3+900 e^{\frac {2 e^{2 x}}{x^2}} x^3+150 e^{\frac {3 e^{2 x}}{x^2}} x^3-720 e^{\frac {e^{2 x}}{x^2}} x^2-640 e^{\frac {2 e^{2 x}}{x^2}} x^2-150 e^{\frac {3 e^{2 x}}{x^2}} x^2+x^2+81 e^{\frac {e^{2 x}}{x^2}} x+40 e^{\frac {2 e^{2 x}}{x^2}} x-4 x-e^{\frac {e^{2 x}}{x^2}}+2}{-5 x^3+5 e^{\frac {e^{2 x}}{x^2}} x^2+10 x^2-x+e^x}-\frac {x \left (250 e^{\frac {e^{2 x}}{x^2}} x^7-1750 e^{\frac {e^{2 x}}{x^2}} x^6-750 e^{\frac {2 e^{2 x}}{x^2}} x^6+4600 e^{\frac {e^{2 x}}{x^2}} x^5+3750 e^{\frac {2 e^{2 x}}{x^2}} x^5+750 e^{\frac {3 e^{2 x}}{x^2}} x^5-5500 e^{\frac {e^{2 x}}{x^2}} x^4-6200 e^{\frac {2 e^{2 x}}{x^2}} x^4-2250 e^{\frac {3 e^{2 x}}{x^2}} x^4-250 e^{\frac {4 e^{2 x}}{x^2}} x^4+5 x^4+2800 e^{\frac {e^{2 x}}{x^2}} x^3+3600 e^{\frac {2 e^{2 x}}{x^2}} x^3+1600 e^{\frac {3 e^{2 x}}{x^2}} x^3+250 e^{\frac {4 e^{2 x}}{x^2}} x^3-35 x^3-385 e^{\frac {e^{2 x}}{x^2}} x^2-405 e^{\frac {2 e^{2 x}}{x^2}} x^2-100 e^{\frac {3 e^{2 x}}{x^2}} x^2+71 x^2-21 e^{\frac {e^{2 x}}{x^2}} x-43 x+e^{\frac {e^{2 x}}{x^2}}+2\right )}{\left (5 x^3-5 e^{\frac {e^{2 x}}{x^2}} x^2-10 x^2+x-e^x\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 20 \int \frac {5 e^{\frac {2 e^{2 x}}{x^2}} x^4-10 e^{\frac {e^{2 x}}{x^2}} (x-2) x^4+\left (5 x^2-20 x+19\right ) x^4+e^{x+\frac {e^{2 x}}{x^2}} (x-1) x^2-e^x \left (x^2-4 x+2\right ) x^2+2 e^{2 x+\frac {e^{2 x}}{x^2}} (x-1) x-2 e^{3 x+\frac {e^{2 x}}{x^2}} (x-1)}{x^2 \left (5 e^{\frac {e^{2 x}}{x^2}} x^2+\left (-5 x^2+10 x-1\right ) x+e^x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 20 \int \left (\frac {2 e^{\frac {e^{2 x}}{x^2}} \left (-10 x^2+10 e^{\frac {e^{2 x}}{x^2}} x+20 x-1\right ) (x-1)}{x}-\frac {2 e^{x+\frac {e^{2 x}}{x^2}} (x-1)}{x^2}-\frac {150 e^{\frac {e^{2 x}}{x^2}} x^5-750 e^{\frac {e^{2 x}}{x^2}} x^4-300 e^{\frac {2 e^{2 x}}{x^2}} x^4+1240 e^{\frac {e^{2 x}}{x^2}} x^3+900 e^{\frac {2 e^{2 x}}{x^2}} x^3+150 e^{\frac {3 e^{2 x}}{x^2}} x^3-720 e^{\frac {e^{2 x}}{x^2}} x^2-640 e^{\frac {2 e^{2 x}}{x^2}} x^2-150 e^{\frac {3 e^{2 x}}{x^2}} x^2+x^2+81 e^{\frac {e^{2 x}}{x^2}} x+40 e^{\frac {2 e^{2 x}}{x^2}} x-4 x-e^{\frac {e^{2 x}}{x^2}}+2}{-5 x^3+5 e^{\frac {e^{2 x}}{x^2}} x^2+10 x^2-x+e^x}-\frac {x \left (250 e^{\frac {e^{2 x}}{x^2}} x^7-1750 e^{\frac {e^{2 x}}{x^2}} x^6-750 e^{\frac {2 e^{2 x}}{x^2}} x^6+4600 e^{\frac {e^{2 x}}{x^2}} x^5+3750 e^{\frac {2 e^{2 x}}{x^2}} x^5+750 e^{\frac {3 e^{2 x}}{x^2}} x^5-5500 e^{\frac {e^{2 x}}{x^2}} x^4-6200 e^{\frac {2 e^{2 x}}{x^2}} x^4-2250 e^{\frac {3 e^{2 x}}{x^2}} x^4-250 e^{\frac {4 e^{2 x}}{x^2}} x^4+5 x^4+2800 e^{\frac {e^{2 x}}{x^2}} x^3+3600 e^{\frac {2 e^{2 x}}{x^2}} x^3+1600 e^{\frac {3 e^{2 x}}{x^2}} x^3+250 e^{\frac {4 e^{2 x}}{x^2}} x^3-35 x^3-385 e^{\frac {e^{2 x}}{x^2}} x^2-405 e^{\frac {2 e^{2 x}}{x^2}} x^2-100 e^{\frac {3 e^{2 x}}{x^2}} x^2+71 x^2-21 e^{\frac {e^{2 x}}{x^2}} x-43 x+e^{\frac {e^{2 x}}{x^2}}+2\right )}{\left (5 x^3-5 e^{\frac {e^{2 x}}{x^2}} x^2-10 x^2+x-e^x\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 20 \int \frac {5 e^{\frac {2 e^{2 x}}{x^2}} x^4-10 e^{\frac {e^{2 x}}{x^2}} (x-2) x^4+\left (5 x^2-20 x+19\right ) x^4+e^{x+\frac {e^{2 x}}{x^2}} (x-1) x^2-e^x \left (x^2-4 x+2\right ) x^2+2 e^{2 x+\frac {e^{2 x}}{x^2}} (x-1) x-2 e^{3 x+\frac {e^{2 x}}{x^2}} (x-1)}{x^2 \left (5 e^{\frac {e^{2 x}}{x^2}} x^2+\left (-5 x^2+10 x-1\right ) x+e^x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 20 \int \left (\frac {2 e^{\frac {e^{2 x}}{x^2}} \left (-10 x^2+10 e^{\frac {e^{2 x}}{x^2}} x+20 x-1\right ) (x-1)}{x}-\frac {2 e^{x+\frac {e^{2 x}}{x^2}} (x-1)}{x^2}-\frac {150 e^{\frac {e^{2 x}}{x^2}} x^5-750 e^{\frac {e^{2 x}}{x^2}} x^4-300 e^{\frac {2 e^{2 x}}{x^2}} x^4+1240 e^{\frac {e^{2 x}}{x^2}} x^3+900 e^{\frac {2 e^{2 x}}{x^2}} x^3+150 e^{\frac {3 e^{2 x}}{x^2}} x^3-720 e^{\frac {e^{2 x}}{x^2}} x^2-640 e^{\frac {2 e^{2 x}}{x^2}} x^2-150 e^{\frac {3 e^{2 x}}{x^2}} x^2+x^2+81 e^{\frac {e^{2 x}}{x^2}} x+40 e^{\frac {2 e^{2 x}}{x^2}} x-4 x-e^{\frac {e^{2 x}}{x^2}}+2}{-5 x^3+5 e^{\frac {e^{2 x}}{x^2}} x^2+10 x^2-x+e^x}-\frac {x \left (250 e^{\frac {e^{2 x}}{x^2}} x^7-1750 e^{\frac {e^{2 x}}{x^2}} x^6-750 e^{\frac {2 e^{2 x}}{x^2}} x^6+4600 e^{\frac {e^{2 x}}{x^2}} x^5+3750 e^{\frac {2 e^{2 x}}{x^2}} x^5+750 e^{\frac {3 e^{2 x}}{x^2}} x^5-5500 e^{\frac {e^{2 x}}{x^2}} x^4-6200 e^{\frac {2 e^{2 x}}{x^2}} x^4-2250 e^{\frac {3 e^{2 x}}{x^2}} x^4-250 e^{\frac {4 e^{2 x}}{x^2}} x^4+5 x^4+2800 e^{\frac {e^{2 x}}{x^2}} x^3+3600 e^{\frac {2 e^{2 x}}{x^2}} x^3+1600 e^{\frac {3 e^{2 x}}{x^2}} x^3+250 e^{\frac {4 e^{2 x}}{x^2}} x^3-35 x^3-385 e^{\frac {e^{2 x}}{x^2}} x^2-405 e^{\frac {2 e^{2 x}}{x^2}} x^2-100 e^{\frac {3 e^{2 x}}{x^2}} x^2+71 x^2-21 e^{\frac {e^{2 x}}{x^2}} x-43 x+e^{\frac {e^{2 x}}{x^2}}+2\right )}{\left (5 x^3-5 e^{\frac {e^{2 x}}{x^2}} x^2-10 x^2+x-e^x\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 20 \int \frac {5 e^{\frac {2 e^{2 x}}{x^2}} x^4-10 e^{\frac {e^{2 x}}{x^2}} (x-2) x^4+\left (5 x^2-20 x+19\right ) x^4+e^{x+\frac {e^{2 x}}{x^2}} (x-1) x^2-e^x \left (x^2-4 x+2\right ) x^2+2 e^{2 x+\frac {e^{2 x}}{x^2}} (x-1) x-2 e^{3 x+\frac {e^{2 x}}{x^2}} (x-1)}{x^2 \left (5 e^{\frac {e^{2 x}}{x^2}} x^2+\left (-5 x^2+10 x-1\right ) x+e^x\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 20 \int \left (\frac {2 e^{\frac {e^{2 x}}{x^2}} \left (-10 x^2+10 e^{\frac {e^{2 x}}{x^2}} x+20 x-1\right ) (x-1)}{x}-\frac {2 e^{x+\frac {e^{2 x}}{x^2}} (x-1)}{x^2}-\frac {150 e^{\frac {e^{2 x}}{x^2}} x^5-750 e^{\frac {e^{2 x}}{x^2}} x^4-300 e^{\frac {2 e^{2 x}}{x^2}} x^4+1240 e^{\frac {e^{2 x}}{x^2}} x^3+900 e^{\frac {2 e^{2 x}}{x^2}} x^3+150 e^{\frac {3 e^{2 x}}{x^2}} x^3-720 e^{\frac {e^{2 x}}{x^2}} x^2-640 e^{\frac {2 e^{2 x}}{x^2}} x^2-150 e^{\frac {3 e^{2 x}}{x^2}} x^2+x^2+81 e^{\frac {e^{2 x}}{x^2}} x+40 e^{\frac {2 e^{2 x}}{x^2}} x-4 x-e^{\frac {e^{2 x}}{x^2}}+2}{-5 x^3+5 e^{\frac {e^{2 x}}{x^2}} x^2+10 x^2-x+e^x}-\frac {x \left (250 e^{\frac {e^{2 x}}{x^2}} x^7-1750 e^{\frac {e^{2 x}}{x^2}} x^6-750 e^{\frac {2 e^{2 x}}{x^2}} x^6+4600 e^{\frac {e^{2 x}}{x^2}} x^5+3750 e^{\frac {2 e^{2 x}}{x^2}} x^5+750 e^{\frac {3 e^{2 x}}{x^2}} x^5-5500 e^{\frac {e^{2 x}}{x^2}} x^4-6200 e^{\frac {2 e^{2 x}}{x^2}} x^4-2250 e^{\frac {3 e^{2 x}}{x^2}} x^4-250 e^{\frac {4 e^{2 x}}{x^2}} x^4+5 x^4+2800 e^{\frac {e^{2 x}}{x^2}} x^3+3600 e^{\frac {2 e^{2 x}}{x^2}} x^3+1600 e^{\frac {3 e^{2 x}}{x^2}} x^3+250 e^{\frac {4 e^{2 x}}{x^2}} x^3-35 x^3-385 e^{\frac {e^{2 x}}{x^2}} x^2-405 e^{\frac {2 e^{2 x}}{x^2}} x^2-100 e^{\frac {3 e^{2 x}}{x^2}} x^2+71 x^2-21 e^{\frac {e^{2 x}}{x^2}} x-43 x+e^{\frac {e^{2 x}}{x^2}}+2\right )}{\left (5 x^3-5 e^{\frac {e^{2 x}}{x^2}} x^2-10 x^2+x-e^x\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 20 \int \frac {5 e^{\frac {2 e^{2 x}}{x^2}} x^4-10 e^{\frac {e^{2 x}}{x^2}} (x-2) x^4+\left (5 x^2-20 x+19\right ) x^4+e^{x+\frac {e^{2 x}}{x^2}} (x-1) x^2-e^x \left (x^2-4 x+2\right ) x^2+2 e^{2 x+\frac {e^{2 x}}{x^2}} (x-1) x-2 e^{3 x+\frac {e^{2 x}}{x^2}} (x-1)}{x^2 \left (5 e^{\frac {e^{2 x}}{x^2}} x^2+\left (-5 x^2+10 x-1\right ) x+e^x\right )^2}dx\) |
Input:
Int[(380*x^4 + 100*E^((2*E^(2*x))/x^2)*x^4 - 400*x^5 + 100*x^6 + E^x*(-40* x^2 + 80*x^3 - 20*x^4) + E^(E^(2*x)/x^2)*(E^(3*x)*(40 - 40*x) + 400*x^4 - 200*x^5 + E^(2*x)*(-40*x + 40*x^2) + E^x*(-20*x^2 + 20*x^3)))/(E^(2*x)*x^2 + x^4 - 20*x^5 + 110*x^6 + 25*E^((2*E^(2*x))/x^2)*x^6 - 100*x^7 + 25*x^8 + E^x*(-2*x^3 + 20*x^4 - 10*x^5) + E^(E^(2*x)/x^2)*(10*E^x*x^4 - 10*x^5 + 100*x^6 - 50*x^7)),x]
Output:
$Aborted
Time = 2.42 (sec) , antiderivative size = 50, normalized size of antiderivative = 1.19
| method | result | size |
| risch | \(-\frac {4}{x}+\frac {4 x -4 \,{\mathrm e}^{x}}{x \left (5 x^{3}-5 x^{2} {\mathrm e}^{\frac {{\mathrm e}^{2 x}}{x^{2}}}-10 x^{2}+x -{\mathrm e}^{x}\right )}\) | \(50\) |
| parallelrisch | \(-\frac {100 x^{2}-100 x \,{\mathrm e}^{\frac {{\mathrm e}^{2 x}}{x^{2}}}-200 x}{5 \left (5 x^{3}-5 x^{2} {\mathrm e}^{\frac {{\mathrm e}^{2 x}}{x^{2}}}-10 x^{2}+x -{\mathrm e}^{x}\right )}\) | \(56\) |
Input:
int((100*x^4*exp(exp(x)^2/x^2)^2+((-40*x+40)*exp(x)^3+(40*x^2-40*x)*exp(x) ^2+(20*x^3-20*x^2)*exp(x)-200*x^5+400*x^4)*exp(exp(x)^2/x^2)+(-20*x^4+80*x ^3-40*x^2)*exp(x)+100*x^6-400*x^5+380*x^4)/(25*x^6*exp(exp(x)^2/x^2)^2+(10 *exp(x)*x^4-50*x^7+100*x^6-10*x^5)*exp(exp(x)^2/x^2)+exp(x)^2*x^2+(-10*x^5 +20*x^4-2*x^3)*exp(x)+25*x^8-100*x^7+110*x^6-20*x^5+x^4),x,method=_RETURNV ERBOSE)
Output:
-4/x+4*(x-exp(x))/x/(5*x^3-5*x^2*exp(exp(2*x)/x^2)-10*x^2+x-exp(x))
Time = 0.10 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.26 \[ \int \frac {380 x^4+100 e^{\frac {2 e^{2 x}}{x^2}} x^4-400 x^5+100 x^6+e^x \left (-40 x^2+80 x^3-20 x^4\right )+e^{\frac {e^{2 x}}{x^2}} \left (e^{3 x} (40-40 x)+400 x^4-200 x^5+e^{2 x} \left (-40 x+40 x^2\right )+e^x \left (-20 x^2+20 x^3\right )\right )}{e^{2 x} x^2+x^4-20 x^5+110 x^6+25 e^{\frac {2 e^{2 x}}{x^2}} x^6-100 x^7+25 x^8+e^x \left (-2 x^3+20 x^4-10 x^5\right )+e^{\frac {e^{2 x}}{x^2}} \left (10 e^x x^4-10 x^5+100 x^6-50 x^7\right )} \, dx=-\frac {20 \, {\left (x^{2} - x e^{\left (\frac {e^{\left (2 \, x\right )}}{x^{2}}\right )} - 2 \, x\right )}}{5 \, x^{3} - 5 \, x^{2} e^{\left (\frac {e^{\left (2 \, x\right )}}{x^{2}}\right )} - 10 \, x^{2} + x - e^{x}} \] Input:
integrate((100*x^4*exp(exp(x)^2/x^2)^2+((-40*x+40)*exp(x)^3+(40*x^2-40*x)* exp(x)^2+(20*x^3-20*x^2)*exp(x)-200*x^5+400*x^4)*exp(exp(x)^2/x^2)+(-20*x^ 4+80*x^3-40*x^2)*exp(x)+100*x^6-400*x^5+380*x^4)/(25*x^6*exp(exp(x)^2/x^2) ^2+(10*exp(x)*x^4-50*x^7+100*x^6-10*x^5)*exp(exp(x)^2/x^2)+exp(x)^2*x^2+(- 10*x^5+20*x^4-2*x^3)*exp(x)+25*x^8-100*x^7+110*x^6-20*x^5+x^4),x, algorith m="fricas")
Output:
-20*(x^2 - x*e^(e^(2*x)/x^2) - 2*x)/(5*x^3 - 5*x^2*e^(e^(2*x)/x^2) - 10*x^ 2 + x - e^x)
Time = 0.20 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.05 \[ \int \frac {380 x^4+100 e^{\frac {2 e^{2 x}}{x^2}} x^4-400 x^5+100 x^6+e^x \left (-40 x^2+80 x^3-20 x^4\right )+e^{\frac {e^{2 x}}{x^2}} \left (e^{3 x} (40-40 x)+400 x^4-200 x^5+e^{2 x} \left (-40 x+40 x^2\right )+e^x \left (-20 x^2+20 x^3\right )\right )}{e^{2 x} x^2+x^4-20 x^5+110 x^6+25 e^{\frac {2 e^{2 x}}{x^2}} x^6-100 x^7+25 x^8+e^x \left (-2 x^3+20 x^4-10 x^5\right )+e^{\frac {e^{2 x}}{x^2}} \left (10 e^x x^4-10 x^5+100 x^6-50 x^7\right )} \, dx=\frac {- 4 x + 4 e^{x}}{- 5 x^{4} + 5 x^{3} e^{\frac {e^{2 x}}{x^{2}}} + 10 x^{3} - x^{2} + x e^{x}} - \frac {4}{x} \] Input:
integrate((100*x**4*exp(exp(x)**2/x**2)**2+((-40*x+40)*exp(x)**3+(40*x**2- 40*x)*exp(x)**2+(20*x**3-20*x**2)*exp(x)-200*x**5+400*x**4)*exp(exp(x)**2/ x**2)+(-20*x**4+80*x**3-40*x**2)*exp(x)+100*x**6-400*x**5+380*x**4)/(25*x* *6*exp(exp(x)**2/x**2)**2+(10*exp(x)*x**4-50*x**7+100*x**6-10*x**5)*exp(ex p(x)**2/x**2)+exp(x)**2*x**2+(-10*x**5+20*x**4-2*x**3)*exp(x)+25*x**8-100* x**7+110*x**6-20*x**5+x**4),x)
Output:
(-4*x + 4*exp(x))/(-5*x**4 + 5*x**3*exp(exp(2*x)/x**2) + 10*x**3 - x**2 + x*exp(x)) - 4/x
Time = 0.15 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.26 \[ \int \frac {380 x^4+100 e^{\frac {2 e^{2 x}}{x^2}} x^4-400 x^5+100 x^6+e^x \left (-40 x^2+80 x^3-20 x^4\right )+e^{\frac {e^{2 x}}{x^2}} \left (e^{3 x} (40-40 x)+400 x^4-200 x^5+e^{2 x} \left (-40 x+40 x^2\right )+e^x \left (-20 x^2+20 x^3\right )\right )}{e^{2 x} x^2+x^4-20 x^5+110 x^6+25 e^{\frac {2 e^{2 x}}{x^2}} x^6-100 x^7+25 x^8+e^x \left (-2 x^3+20 x^4-10 x^5\right )+e^{\frac {e^{2 x}}{x^2}} \left (10 e^x x^4-10 x^5+100 x^6-50 x^7\right )} \, dx=-\frac {20 \, {\left (x^{2} - x e^{\left (\frac {e^{\left (2 \, x\right )}}{x^{2}}\right )} - 2 \, x\right )}}{5 \, x^{3} - 5 \, x^{2} e^{\left (\frac {e^{\left (2 \, x\right )}}{x^{2}}\right )} - 10 \, x^{2} + x - e^{x}} \] Input:
integrate((100*x^4*exp(exp(x)^2/x^2)^2+((-40*x+40)*exp(x)^3+(40*x^2-40*x)* exp(x)^2+(20*x^3-20*x^2)*exp(x)-200*x^5+400*x^4)*exp(exp(x)^2/x^2)+(-20*x^ 4+80*x^3-40*x^2)*exp(x)+100*x^6-400*x^5+380*x^4)/(25*x^6*exp(exp(x)^2/x^2) ^2+(10*exp(x)*x^4-50*x^7+100*x^6-10*x^5)*exp(exp(x)^2/x^2)+exp(x)^2*x^2+(- 10*x^5+20*x^4-2*x^3)*exp(x)+25*x^8-100*x^7+110*x^6-20*x^5+x^4),x, algorith m="maxima")
Output:
-20*(x^2 - x*e^(e^(2*x)/x^2) - 2*x)/(5*x^3 - 5*x^2*e^(e^(2*x)/x^2) - 10*x^ 2 + x - e^x)
Leaf count of result is larger than twice the leaf count of optimal. 708 vs. \(2 (36) = 72\).
Time = 0.34 (sec) , antiderivative size = 708, normalized size of antiderivative = 16.86 \[ \int \frac {380 x^4+100 e^{\frac {2 e^{2 x}}{x^2}} x^4-400 x^5+100 x^6+e^x \left (-40 x^2+80 x^3-20 x^4\right )+e^{\frac {e^{2 x}}{x^2}} \left (e^{3 x} (40-40 x)+400 x^4-200 x^5+e^{2 x} \left (-40 x+40 x^2\right )+e^x \left (-20 x^2+20 x^3\right )\right )}{e^{2 x} x^2+x^4-20 x^5+110 x^6+25 e^{\frac {2 e^{2 x}}{x^2}} x^6-100 x^7+25 x^8+e^x \left (-2 x^3+20 x^4-10 x^5\right )+e^{\frac {e^{2 x}}{x^2}} \left (10 e^x x^4-10 x^5+100 x^6-50 x^7\right )} \, dx =\text {Too large to display} \] Input:
integrate((100*x^4*exp(exp(x)^2/x^2)^2+((-40*x+40)*exp(x)^3+(40*x^2-40*x)* exp(x)^2+(20*x^3-20*x^2)*exp(x)-200*x^5+400*x^4)*exp(exp(x)^2/x^2)+(-20*x^ 4+80*x^3-40*x^2)*exp(x)+100*x^6-400*x^5+380*x^4)/(25*x^6*exp(exp(x)^2/x^2) ^2+(10*exp(x)*x^4-50*x^7+100*x^6-10*x^5)*exp(exp(x)^2/x^2)+exp(x)^2*x^2+(- 10*x^5+20*x^4-2*x^3)*exp(x)+25*x^8-100*x^7+110*x^6-20*x^5+x^4),x, algorith m="giac")
Output:
-20*(5*x^8*e^x - 10*x^7*e^(3*x) - 10*x^7*e^x - 5*x^7*e^((x^3 + e^(2*x))/x^ 2) + 50*x^6*e^(3*x) - x^6*e^(2*x) + 10*x^6*e^(2*x + (x^3 + e^(2*x))/x^2) - x^6*e^x - 82*x^5*e^(3*x) + 4*x^5*e^(2*x) - 30*x^5*e^(2*x + (x^3 + e^(2*x) )/x^2) + x^5*e^(x + (x^3 + e^(2*x))/x^2) + 2*x^5*e^x + x^5*e^((x^3 + e^(2* x))/x^2) + 2*x^4*e^(4*x) + 46*x^4*e^(3*x) - 4*x^4*e^(2*x) + 22*x^4*e^(2*x + (x^3 + e^(2*x))/x^2) - 2*x^4*e^(x + (x^3 + e^(2*x))/x^2) - 6*x^3*e^(4*x) - 4*x^3*e^(3*x) - 2*x^3*e^(3*x + (x^3 + e^(2*x))/x^2) - 2*x^3*e^(2*x + (x ^3 + e^(2*x))/x^2) + 4*x^2*e^(4*x) + 2*x^2*e^(3*x + (x^3 + e^(2*x))/x^2))/ (25*x^9*e^x - 50*x^8*e^(3*x) - 50*x^8*e^x - 25*x^8*e^((x^3 + e^(2*x))/x^2) + 250*x^7*e^(3*x) - 5*x^7*e^(2*x) + 50*x^7*e^(2*x + (x^3 + e^(2*x))/x^2) - 420*x^6*e^(3*x) + 15*x^6*e^(2*x) - 150*x^6*e^(2*x + (x^3 + e^(2*x))/x^2) + 5*x^6*e^(x + (x^3 + e^(2*x))/x^2) + 10*x^6*e^x + 5*x^6*e^((x^3 + e^(2*x ))/x^2) + 20*x^5*e^(4*x) + 260*x^5*e^(3*x) - 21*x^5*e^(2*x) + 110*x^5*e^(2 *x + (x^3 + e^(2*x))/x^2) - 10*x^5*e^(x + (x^3 + e^(2*x))/x^2) - x^5*e^x - 60*x^4*e^(4*x) - 41*x^4*e^(3*x) + 3*x^4*e^(2*x) - 10*x^4*e^(3*x + (x^3 + e^(2*x))/x^2) - 10*x^4*e^(2*x + (x^3 + e^(2*x))/x^2) + 44*x^3*e^(4*x) + 10 *x^3*e^(3*x + (x^3 + e^(2*x))/x^2) - 2*x^2*e^(5*x) - 4*x^2*e^(4*x) + 2*x*e ^(5*x))
Time = 3.14 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.17 \[ \int \frac {380 x^4+100 e^{\frac {2 e^{2 x}}{x^2}} x^4-400 x^5+100 x^6+e^x \left (-40 x^2+80 x^3-20 x^4\right )+e^{\frac {e^{2 x}}{x^2}} \left (e^{3 x} (40-40 x)+400 x^4-200 x^5+e^{2 x} \left (-40 x+40 x^2\right )+e^x \left (-20 x^2+20 x^3\right )\right )}{e^{2 x} x^2+x^4-20 x^5+110 x^6+25 e^{\frac {2 e^{2 x}}{x^2}} x^6-100 x^7+25 x^8+e^x \left (-2 x^3+20 x^4-10 x^5\right )+e^{\frac {e^{2 x}}{x^2}} \left (10 e^x x^4-10 x^5+100 x^6-50 x^7\right )} \, dx=-\frac {20\,x\,\left ({\mathrm {e}}^{\frac {{\mathrm {e}}^{2\,x}}{x^2}}-x+2\right )}{{\mathrm {e}}^x-x+5\,x^2\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{2\,x}}{x^2}}+10\,x^2-5\,x^3} \] Input:
int((100*x^4*exp((2*exp(2*x))/x^2) - exp(x)*(40*x^2 - 80*x^3 + 20*x^4) + 3 80*x^4 - 400*x^5 + 100*x^6 - exp(exp(2*x)/x^2)*(exp(2*x)*(40*x - 40*x^2) + exp(x)*(20*x^2 - 20*x^3) + exp(3*x)*(40*x - 40) - 400*x^4 + 200*x^5))/(25 *x^6*exp((2*exp(2*x))/x^2) - exp(x)*(2*x^3 - 20*x^4 + 10*x^5) + exp(exp(2* x)/x^2)*(10*x^4*exp(x) - 10*x^5 + 100*x^6 - 50*x^7) + x^2*exp(2*x) + x^4 - 20*x^5 + 110*x^6 - 100*x^7 + 25*x^8),x)
Output:
-(20*x*(exp(exp(2*x)/x^2) - x + 2))/(exp(x) - x + 5*x^2*exp(exp(2*x)/x^2) + 10*x^2 - 5*x^3)
Time = 0.17 (sec) , antiderivative size = 83, normalized size of antiderivative = 1.98 \[ \int \frac {380 x^4+100 e^{\frac {2 e^{2 x}}{x^2}} x^4-400 x^5+100 x^6+e^x \left (-40 x^2+80 x^3-20 x^4\right )+e^{\frac {e^{2 x}}{x^2}} \left (e^{3 x} (40-40 x)+400 x^4-200 x^5+e^{2 x} \left (-40 x+40 x^2\right )+e^x \left (-20 x^2+20 x^3\right )\right )}{e^{2 x} x^2+x^4-20 x^5+110 x^6+25 e^{\frac {2 e^{2 x}}{x^2}} x^6-100 x^7+25 x^8+e^x \left (-2 x^3+20 x^4-10 x^5\right )+e^{\frac {e^{2 x}}{x^2}} \left (10 e^x x^4-10 x^5+100 x^6-50 x^7\right )} \, dx=\frac {-200 e^{\frac {e^{2 x}}{x^{2}}} x^{2}-20 e^{\frac {e^{2 x}}{x^{2}}} x -40 e^{x}+200 x^{3}-380 x^{2}}{5 e^{\frac {e^{2 x}}{x^{2}}} x^{2}+e^{x}-5 x^{3}+10 x^{2}-x} \] Input:
int((100*x^4*exp(exp(x)^2/x^2)^2+((-40*x+40)*exp(x)^3+(40*x^2-40*x)*exp(x) ^2+(20*x^3-20*x^2)*exp(x)-200*x^5+400*x^4)*exp(exp(x)^2/x^2)+(-20*x^4+80*x ^3-40*x^2)*exp(x)+100*x^6-400*x^5+380*x^4)/(25*x^6*exp(exp(x)^2/x^2)^2+(10 *exp(x)*x^4-50*x^7+100*x^6-10*x^5)*exp(exp(x)^2/x^2)+exp(x)^2*x^2+(-10*x^5 +20*x^4-2*x^3)*exp(x)+25*x^8-100*x^7+110*x^6-20*x^5+x^4),x)
Output:
(20*( - 10*e**(e**(2*x)/x**2)*x**2 - e**(e**(2*x)/x**2)*x - 2*e**x + 10*x* *3 - 19*x**2))/(5*e**(e**(2*x)/x**2)*x**2 + e**x - 5*x**3 + 10*x**2 - x)