Integrand size = 202, antiderivative size = 27 \[ \int \frac {e^{\frac {x^2-50 x^3+645 x^4-502 x^5+150 x^6-20 x^7+x^8+e^{2 x} \left (625-500 x+150 x^2-20 x^3+x^4\right )+e^x \left (-50 x+1270 x^2-1002 x^3+300 x^4-40 x^5+2 x^6\right )}{x^2}} \left (-50 x^3+1290 x^4-1506 x^5+600 x^6-100 x^7+6 x^8+e^{2 x} \left (-1250+1750 x-1000 x^2+280 x^3-38 x^4+2 x^5\right )+e^x \left (50 x-50 x^2+268 x^3-402 x^4+180 x^5-32 x^6+2 x^7\right )\right )}{5 x^3} \, dx=\frac {1}{5} e^{\left (-1+(5-x)^2 \left (\frac {e^x}{x}+x\right )\right )^2} \] Output:
1/5*exp(((exp(x)/x+x)*(5-x)^2-1)^2)
Time = 0.12 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.37 \[ \int \frac {e^{\frac {x^2-50 x^3+645 x^4-502 x^5+150 x^6-20 x^7+x^8+e^{2 x} \left (625-500 x+150 x^2-20 x^3+x^4\right )+e^x \left (-50 x+1270 x^2-1002 x^3+300 x^4-40 x^5+2 x^6\right )}{x^2}} \left (-50 x^3+1290 x^4-1506 x^5+600 x^6-100 x^7+6 x^8+e^{2 x} \left (-1250+1750 x-1000 x^2+280 x^3-38 x^4+2 x^5\right )+e^x \left (50 x-50 x^2+268 x^3-402 x^4+180 x^5-32 x^6+2 x^7\right )\right )}{5 x^3} \, dx=\frac {1}{5} e^{\frac {\left (e^x (-5+x)^2+x \left (-1+25 x-10 x^2+x^3\right )\right )^2}{x^2}} \] Input:
Integrate[(E^((x^2 - 50*x^3 + 645*x^4 - 502*x^5 + 150*x^6 - 20*x^7 + x^8 + E^(2*x)*(625 - 500*x + 150*x^2 - 20*x^3 + x^4) + E^x*(-50*x + 1270*x^2 - 1002*x^3 + 300*x^4 - 40*x^5 + 2*x^6))/x^2)*(-50*x^3 + 1290*x^4 - 1506*x^5 + 600*x^6 - 100*x^7 + 6*x^8 + E^(2*x)*(-1250 + 1750*x - 1000*x^2 + 280*x^3 - 38*x^4 + 2*x^5) + E^x*(50*x - 50*x^2 + 268*x^3 - 402*x^4 + 180*x^5 - 32 *x^6 + 2*x^7)))/(5*x^3),x]
Output:
E^((E^x*(-5 + x)^2 + x*(-1 + 25*x - 10*x^2 + x^3))^2/x^2)/5
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.
| \(\displaystyle \int \frac {\left (6 x^8-100 x^7+600 x^6-1506 x^5+1290 x^4-50 x^3+e^{2 x} \left (2 x^5-38 x^4+280 x^3-1000 x^2+1750 x-1250\right )+e^x \left (2 x^7-32 x^6+180 x^5-402 x^4+268 x^3-50 x^2+50 x\right )\right ) \exp \left (\frac {x^8-20 x^7+150 x^6-502 x^5+645 x^4-50 x^3+x^2+e^{2 x} \left (x^4-20 x^3+150 x^2-500 x+625\right )+e^x \left (2 x^6-40 x^5+300 x^4-1002 x^3+1270 x^2-50 x\right )}{x^2}\right )}{5 x^3} \, dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{5} \int -\frac {2 \exp \left (\frac {x^8-20 x^7+150 x^6-502 x^5+645 x^4-50 x^3+x^2+e^{2 x} \left (x^4-20 x^3+150 x^2-500 x+625\right )-2 e^x \left (-x^6+20 x^5-150 x^4+501 x^3-635 x^2+25 x\right )}{x^2}\right ) \left (-3 x^8+50 x^7-300 x^6+753 x^5-645 x^4+25 x^3+e^{2 x} \left (-x^5+19 x^4-140 x^3+500 x^2-875 x+625\right )-e^x \left (x^7-16 x^6+90 x^5-201 x^4+134 x^3-25 x^2+25 x\right )\right )}{x^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle -\frac {2}{5} \int \frac {\exp \left (\frac {x^8-20 x^7+150 x^6-502 x^5+645 x^4-50 x^3+x^2+e^{2 x} \left (x^4-20 x^3+150 x^2-500 x+625\right )-2 e^x \left (-x^6+20 x^5-150 x^4+501 x^3-635 x^2+25 x\right )}{x^2}\right ) \left (-3 x^8+50 x^7-300 x^6+753 x^5-645 x^4+25 x^3+e^{2 x} \left (-x^5+19 x^4-140 x^3+500 x^2-875 x+625\right )-e^x \left (x^7-16 x^6+90 x^5-201 x^4+134 x^3-25 x^2+25 x\right )\right )}{x^3}dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {2}{5} \int \frac {\exp \left (\frac {\left (e^x (x-5)^2+x \left (x^3-10 x^2+25 x-1\right )\right )^2}{x^2}\right ) (5-x) \left (\left (3 x^4-35 x^3+125 x^2-128 x+5\right ) x^3+e^x \left (x^5-11 x^4+35 x^3-26 x^2+4 x-5\right ) x+e^{2 x} (x-5)^2 \left (x^2-4 x+5\right )\right )}{x^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {2}{5} \int \left (-\frac {\exp \left (\frac {\left (e^x (x-5)^2+x \left (x^3-10 x^2+25 x-1\right )\right )^2}{x^2}+2 x\right ) \left (x^2-4 x+5\right ) (x-5)^3}{x^3}-\exp \left (\frac {\left (e^x (x-5)^2+x \left (x^3-10 x^2+25 x-1\right )\right )^2}{x^2}\right ) (3 x-5) \left (x^3-10 x^2+25 x-1\right ) (x-5)-\frac {\exp \left (\frac {\left (e^x (x-5)^2+x \left (x^3-10 x^2+25 x-1\right )\right )^2}{x^2}+x\right ) \left (x^5-11 x^4+35 x^3-26 x^2+4 x-5\right ) (x-5)}{x^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -\frac {2}{5} \left (25 \int e^{\frac {\left (e^x (x-5)^2+x \left (x^3-10 x^2+25 x-1\right )\right )^2}{x^2}}dx-134 \int e^{\frac {\left (e^x (x-5)^2+x \left (x^3-10 x^2+25 x-1\right )\right )^2}{x^2}+x}dx-140 \int e^{\frac {\left (e^x (x-5)^2+x \left (x^3-10 x^2+25 x-1\right )\right )^2}{x^2}+2 x}dx+625 \int \frac {e^{\frac {\left (e^x (x-5)^2+x \left (x^3-10 x^2+25 x-1\right )\right )^2}{x^2}+2 x}}{x^3}dx-25 \int \frac {e^{\frac {\left (e^x (x-5)^2+x \left (x^3-10 x^2+25 x-1\right )\right )^2}{x^2}+x}}{x^2}dx-875 \int \frac {e^{\frac {\left (e^x (x-5)^2+x \left (x^3-10 x^2+25 x-1\right )\right )^2}{x^2}+2 x}}{x^2}dx+25 \int \frac {e^{\frac {\left (e^x (x-5)^2+x \left (x^3-10 x^2+25 x-1\right )\right )^2}{x^2}+x}}{x}dx+500 \int \frac {e^{\frac {\left (e^x (x-5)^2+x \left (x^3-10 x^2+25 x-1\right )\right )^2}{x^2}+2 x}}{x}dx-645 \int e^{\frac {\left (e^x (x-5)^2+x \left (x^3-10 x^2+25 x-1\right )\right )^2}{x^2}} xdx+201 \int e^{\frac {\left (e^x (x-5)^2+x \left (x^3-10 x^2+25 x-1\right )\right )^2}{x^2}+x} xdx+19 \int e^{\frac {\left (e^x (x-5)^2+x \left (x^3-10 x^2+25 x-1\right )\right )^2}{x^2}+2 x} xdx+753 \int e^{\frac {\left (e^x (x-5)^2+x \left (x^3-10 x^2+25 x-1\right )\right )^2}{x^2}} x^2dx-90 \int e^{\frac {\left (e^x (x-5)^2+x \left (x^3-10 x^2+25 x-1\right )\right )^2}{x^2}+x} x^2dx-\int e^{\frac {\left (e^x (x-5)^2+x \left (x^3-10 x^2+25 x-1\right )\right )^2}{x^2}+2 x} x^2dx-300 \int e^{\frac {\left (e^x (x-5)^2+x \left (x^3-10 x^2+25 x-1\right )\right )^2}{x^2}} x^3dx+16 \int e^{\frac {\left (e^x (x-5)^2+x \left (x^3-10 x^2+25 x-1\right )\right )^2}{x^2}+x} x^3dx+50 \int e^{\frac {\left (e^x (x-5)^2+x \left (x^3-10 x^2+25 x-1\right )\right )^2}{x^2}} x^4dx-\int e^{\frac {\left (e^x (x-5)^2+x \left (x^3-10 x^2+25 x-1\right )\right )^2}{x^2}+x} x^4dx-3 \int e^{\frac {\left (e^x (x-5)^2+x \left (x^3-10 x^2+25 x-1\right )\right )^2}{x^2}} x^5dx\right )\) |
Input:
Int[(E^((x^2 - 50*x^3 + 645*x^4 - 502*x^5 + 150*x^6 - 20*x^7 + x^8 + E^(2* x)*(625 - 500*x + 150*x^2 - 20*x^3 + x^4) + E^x*(-50*x + 1270*x^2 - 1002*x ^3 + 300*x^4 - 40*x^5 + 2*x^6))/x^2)*(-50*x^3 + 1290*x^4 - 1506*x^5 + 600* x^6 - 100*x^7 + 6*x^8 + E^(2*x)*(-1250 + 1750*x - 1000*x^2 + 280*x^3 - 38* x^4 + 2*x^5) + E^x*(50*x - 50*x^2 + 268*x^3 - 402*x^4 + 180*x^5 - 32*x^6 + 2*x^7)))/(5*x^3),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(94\) vs. \(2(23)=46\).
Time = 1.19 (sec) , antiderivative size = 95, normalized size of antiderivative = 3.52
| method | result | size |
| parallelrisch | \(\frac {{\mathrm e}^{\frac {\left (x^{4}-20 x^{3}+150 x^{2}-500 x +625\right ) {\mathrm e}^{2 x}+\left (2 x^{6}-40 x^{5}+300 x^{4}-1002 x^{3}+1270 x^{2}-50 x \right ) {\mathrm e}^{x}+x^{8}-20 x^{7}+150 x^{6}-502 x^{5}+645 x^{4}-50 x^{3}+x^{2}}{x^{2}}}}{5}\) | \(95\) |
| risch | \(\frac {{\mathrm e}^{\frac {x^{8}+2 \,{\mathrm e}^{x} x^{6}-20 x^{7}-40 x^{5} {\mathrm e}^{x}+150 x^{6}+300 \,{\mathrm e}^{x} x^{4}+{\mathrm e}^{2 x} x^{4}-502 x^{5}-1002 \,{\mathrm e}^{x} x^{3}-20 \,{\mathrm e}^{2 x} x^{3}+645 x^{4}+1270 \,{\mathrm e}^{x} x^{2}+150 \,{\mathrm e}^{2 x} x^{2}-50 x^{3}-50 \,{\mathrm e}^{x} x -500 x \,{\mathrm e}^{2 x}+x^{2}+625 \,{\mathrm e}^{2 x}}{x^{2}}}}{5}\) | \(119\) |
Input:
int(1/5*((2*x^5-38*x^4+280*x^3-1000*x^2+1750*x-1250)*exp(x)^2+(2*x^7-32*x^ 6+180*x^5-402*x^4+268*x^3-50*x^2+50*x)*exp(x)+6*x^8-100*x^7+600*x^6-1506*x ^5+1290*x^4-50*x^3)*exp(((x^4-20*x^3+150*x^2-500*x+625)*exp(x)^2+(2*x^6-40 *x^5+300*x^4-1002*x^3+1270*x^2-50*x)*exp(x)+x^8-20*x^7+150*x^6-502*x^5+645 *x^4-50*x^3+x^2)/x^2)/x^3,x,method=_RETURNVERBOSE)
Output:
1/5*exp(((x^4-20*x^3+150*x^2-500*x+625)*exp(x)^2+(2*x^6-40*x^5+300*x^4-100 2*x^3+1270*x^2-50*x)*exp(x)+x^8-20*x^7+150*x^6-502*x^5+645*x^4-50*x^3+x^2) /x^2)
Leaf count of result is larger than twice the leaf count of optimal. 93 vs. \(2 (21) = 42\).
Time = 0.10 (sec) , antiderivative size = 93, normalized size of antiderivative = 3.44 \[ \int \frac {e^{\frac {x^2-50 x^3+645 x^4-502 x^5+150 x^6-20 x^7+x^8+e^{2 x} \left (625-500 x+150 x^2-20 x^3+x^4\right )+e^x \left (-50 x+1270 x^2-1002 x^3+300 x^4-40 x^5+2 x^6\right )}{x^2}} \left (-50 x^3+1290 x^4-1506 x^5+600 x^6-100 x^7+6 x^8+e^{2 x} \left (-1250+1750 x-1000 x^2+280 x^3-38 x^4+2 x^5\right )+e^x \left (50 x-50 x^2+268 x^3-402 x^4+180 x^5-32 x^6+2 x^7\right )\right )}{5 x^3} \, dx=\frac {1}{5} \, e^{\left (\frac {x^{8} - 20 \, x^{7} + 150 \, x^{6} - 502 \, x^{5} + 645 \, x^{4} - 50 \, x^{3} + x^{2} + {\left (x^{4} - 20 \, x^{3} + 150 \, x^{2} - 500 \, x + 625\right )} e^{\left (2 \, x\right )} + 2 \, {\left (x^{6} - 20 \, x^{5} + 150 \, x^{4} - 501 \, x^{3} + 635 \, x^{2} - 25 \, x\right )} e^{x}}{x^{2}}\right )} \] Input:
integrate(1/5*((2*x^5-38*x^4+280*x^3-1000*x^2+1750*x-1250)*exp(x)^2+(2*x^7 -32*x^6+180*x^5-402*x^4+268*x^3-50*x^2+50*x)*exp(x)+6*x^8-100*x^7+600*x^6- 1506*x^5+1290*x^4-50*x^3)*exp(((x^4-20*x^3+150*x^2-500*x+625)*exp(x)^2+(2* x^6-40*x^5+300*x^4-1002*x^3+1270*x^2-50*x)*exp(x)+x^8-20*x^7+150*x^6-502*x ^5+645*x^4-50*x^3+x^2)/x^2)/x^3,x, algorithm="fricas")
Output:
1/5*e^((x^8 - 20*x^7 + 150*x^6 - 502*x^5 + 645*x^4 - 50*x^3 + x^2 + (x^4 - 20*x^3 + 150*x^2 - 500*x + 625)*e^(2*x) + 2*(x^6 - 20*x^5 + 150*x^4 - 501 *x^3 + 635*x^2 - 25*x)*e^x)/x^2)
Leaf count of result is larger than twice the leaf count of optimal. 94 vs. \(2 (17) = 34\).
Time = 0.39 (sec) , antiderivative size = 94, normalized size of antiderivative = 3.48 \[ \int \frac {e^{\frac {x^2-50 x^3+645 x^4-502 x^5+150 x^6-20 x^7+x^8+e^{2 x} \left (625-500 x+150 x^2-20 x^3+x^4\right )+e^x \left (-50 x+1270 x^2-1002 x^3+300 x^4-40 x^5+2 x^6\right )}{x^2}} \left (-50 x^3+1290 x^4-1506 x^5+600 x^6-100 x^7+6 x^8+e^{2 x} \left (-1250+1750 x-1000 x^2+280 x^3-38 x^4+2 x^5\right )+e^x \left (50 x-50 x^2+268 x^3-402 x^4+180 x^5-32 x^6+2 x^7\right )\right )}{5 x^3} \, dx=\frac {e^{\frac {x^{8} - 20 x^{7} + 150 x^{6} - 502 x^{5} + 645 x^{4} - 50 x^{3} + x^{2} + \left (x^{4} - 20 x^{3} + 150 x^{2} - 500 x + 625\right ) e^{2 x} + \left (2 x^{6} - 40 x^{5} + 300 x^{4} - 1002 x^{3} + 1270 x^{2} - 50 x\right ) e^{x}}{x^{2}}}}{5} \] Input:
integrate(1/5*((2*x**5-38*x**4+280*x**3-1000*x**2+1750*x-1250)*exp(x)**2+( 2*x**7-32*x**6+180*x**5-402*x**4+268*x**3-50*x**2+50*x)*exp(x)+6*x**8-100* x**7+600*x**6-1506*x**5+1290*x**4-50*x**3)*exp(((x**4-20*x**3+150*x**2-500 *x+625)*exp(x)**2+(2*x**6-40*x**5+300*x**4-1002*x**3+1270*x**2-50*x)*exp(x )+x**8-20*x**7+150*x**6-502*x**5+645*x**4-50*x**3+x**2)/x**2)/x**3,x)
Output:
exp((x**8 - 20*x**7 + 150*x**6 - 502*x**5 + 645*x**4 - 50*x**3 + x**2 + (x **4 - 20*x**3 + 150*x**2 - 500*x + 625)*exp(2*x) + (2*x**6 - 40*x**5 + 300 *x**4 - 1002*x**3 + 1270*x**2 - 50*x)*exp(x))/x**2)/5
Leaf count of result is larger than twice the leaf count of optimal. 107 vs. \(2 (21) = 42\).
Time = 0.53 (sec) , antiderivative size = 107, normalized size of antiderivative = 3.96 \[ \int \frac {e^{\frac {x^2-50 x^3+645 x^4-502 x^5+150 x^6-20 x^7+x^8+e^{2 x} \left (625-500 x+150 x^2-20 x^3+x^4\right )+e^x \left (-50 x+1270 x^2-1002 x^3+300 x^4-40 x^5+2 x^6\right )}{x^2}} \left (-50 x^3+1290 x^4-1506 x^5+600 x^6-100 x^7+6 x^8+e^{2 x} \left (-1250+1750 x-1000 x^2+280 x^3-38 x^4+2 x^5\right )+e^x \left (50 x-50 x^2+268 x^3-402 x^4+180 x^5-32 x^6+2 x^7\right )\right )}{5 x^3} \, dx=\frac {1}{5} \, e^{\left (x^{6} - 20 \, x^{5} + 2 \, x^{4} e^{x} + 150 \, x^{4} - 40 \, x^{3} e^{x} - 502 \, x^{3} + x^{2} e^{\left (2 \, x\right )} + 300 \, x^{2} e^{x} + 645 \, x^{2} - 20 \, x e^{\left (2 \, x\right )} - 1002 \, x e^{x} - 50 \, x - \frac {500 \, e^{\left (2 \, x\right )}}{x} - \frac {50 \, e^{x}}{x} + \frac {625 \, e^{\left (2 \, x\right )}}{x^{2}} + 150 \, e^{\left (2 \, x\right )} + 1270 \, e^{x} + 1\right )} \] Input:
integrate(1/5*((2*x^5-38*x^4+280*x^3-1000*x^2+1750*x-1250)*exp(x)^2+(2*x^7 -32*x^6+180*x^5-402*x^4+268*x^3-50*x^2+50*x)*exp(x)+6*x^8-100*x^7+600*x^6- 1506*x^5+1290*x^4-50*x^3)*exp(((x^4-20*x^3+150*x^2-500*x+625)*exp(x)^2+(2* x^6-40*x^5+300*x^4-1002*x^3+1270*x^2-50*x)*exp(x)+x^8-20*x^7+150*x^6-502*x ^5+645*x^4-50*x^3+x^2)/x^2)/x^3,x, algorithm="maxima")
Output:
1/5*e^(x^6 - 20*x^5 + 2*x^4*e^x + 150*x^4 - 40*x^3*e^x - 502*x^3 + x^2*e^( 2*x) + 300*x^2*e^x + 645*x^2 - 20*x*e^(2*x) - 1002*x*e^x - 50*x - 500*e^(2 *x)/x - 50*e^x/x + 625*e^(2*x)/x^2 + 150*e^(2*x) + 1270*e^x + 1)
\[ \int \frac {e^{\frac {x^2-50 x^3+645 x^4-502 x^5+150 x^6-20 x^7+x^8+e^{2 x} \left (625-500 x+150 x^2-20 x^3+x^4\right )+e^x \left (-50 x+1270 x^2-1002 x^3+300 x^4-40 x^5+2 x^6\right )}{x^2}} \left (-50 x^3+1290 x^4-1506 x^5+600 x^6-100 x^7+6 x^8+e^{2 x} \left (-1250+1750 x-1000 x^2+280 x^3-38 x^4+2 x^5\right )+e^x \left (50 x-50 x^2+268 x^3-402 x^4+180 x^5-32 x^6+2 x^7\right )\right )}{5 x^3} \, dx=\int { \frac {2 \, {\left (3 \, x^{8} - 50 \, x^{7} + 300 \, x^{6} - 753 \, x^{5} + 645 \, x^{4} - 25 \, x^{3} + {\left (x^{5} - 19 \, x^{4} + 140 \, x^{3} - 500 \, x^{2} + 875 \, x - 625\right )} e^{\left (2 \, x\right )} + {\left (x^{7} - 16 \, x^{6} + 90 \, x^{5} - 201 \, x^{4} + 134 \, x^{3} - 25 \, x^{2} + 25 \, x\right )} e^{x}\right )} e^{\left (\frac {x^{8} - 20 \, x^{7} + 150 \, x^{6} - 502 \, x^{5} + 645 \, x^{4} - 50 \, x^{3} + x^{2} + {\left (x^{4} - 20 \, x^{3} + 150 \, x^{2} - 500 \, x + 625\right )} e^{\left (2 \, x\right )} + 2 \, {\left (x^{6} - 20 \, x^{5} + 150 \, x^{4} - 501 \, x^{3} + 635 \, x^{2} - 25 \, x\right )} e^{x}}{x^{2}}\right )}}{5 \, x^{3}} \,d x } \] Input:
integrate(1/5*((2*x^5-38*x^4+280*x^3-1000*x^2+1750*x-1250)*exp(x)^2+(2*x^7 -32*x^6+180*x^5-402*x^4+268*x^3-50*x^2+50*x)*exp(x)+6*x^8-100*x^7+600*x^6- 1506*x^5+1290*x^4-50*x^3)*exp(((x^4-20*x^3+150*x^2-500*x+625)*exp(x)^2+(2* x^6-40*x^5+300*x^4-1002*x^3+1270*x^2-50*x)*exp(x)+x^8-20*x^7+150*x^6-502*x ^5+645*x^4-50*x^3+x^2)/x^2)/x^3,x, algorithm="giac")
Output:
integrate(2/5*(3*x^8 - 50*x^7 + 300*x^6 - 753*x^5 + 645*x^4 - 25*x^3 + (x^ 5 - 19*x^4 + 140*x^3 - 500*x^2 + 875*x - 625)*e^(2*x) + (x^7 - 16*x^6 + 90 *x^5 - 201*x^4 + 134*x^3 - 25*x^2 + 25*x)*e^x)*e^((x^8 - 20*x^7 + 150*x^6 - 502*x^5 + 645*x^4 - 50*x^3 + x^2 + (x^4 - 20*x^3 + 150*x^2 - 500*x + 625 )*e^(2*x) + 2*(x^6 - 20*x^5 + 150*x^4 - 501*x^3 + 635*x^2 - 25*x)*e^x)/x^2 )/x^3, x)
Time = 3.82 (sec) , antiderivative size = 123, normalized size of antiderivative = 4.56 \[ \int \frac {e^{\frac {x^2-50 x^3+645 x^4-502 x^5+150 x^6-20 x^7+x^8+e^{2 x} \left (625-500 x+150 x^2-20 x^3+x^4\right )+e^x \left (-50 x+1270 x^2-1002 x^3+300 x^4-40 x^5+2 x^6\right )}{x^2}} \left (-50 x^3+1290 x^4-1506 x^5+600 x^6-100 x^7+6 x^8+e^{2 x} \left (-1250+1750 x-1000 x^2+280 x^3-38 x^4+2 x^5\right )+e^x \left (50 x-50 x^2+268 x^3-402 x^4+180 x^5-32 x^6+2 x^7\right )\right )}{5 x^3} \, dx=\frac {{\mathrm {e}}^{150\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^{-1002\,x\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-50\,x}\,{\mathrm {e}}^{x^6}\,\mathrm {e}\,{\mathrm {e}}^{-20\,x\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^{2\,x^4\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-40\,x^3\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-\frac {50\,{\mathrm {e}}^x}{x}}\,{\mathrm {e}}^{300\,x^2\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-20\,x^5}\,{\mathrm {e}}^{150\,x^4}\,{\mathrm {e}}^{-502\,x^3}\,{\mathrm {e}}^{645\,x^2}\,{\mathrm {e}}^{1270\,{\mathrm {e}}^x}\,{\mathrm {e}}^{x^2\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^{-\frac {500\,{\mathrm {e}}^{2\,x}}{x}}\,{\mathrm {e}}^{\frac {625\,{\mathrm {e}}^{2\,x}}{x^2}}}{5} \] Input:
int((exp((exp(2*x)*(150*x^2 - 500*x - 20*x^3 + x^4 + 625) - exp(x)*(50*x - 1270*x^2 + 1002*x^3 - 300*x^4 + 40*x^5 - 2*x^6) + x^2 - 50*x^3 + 645*x^4 - 502*x^5 + 150*x^6 - 20*x^7 + x^8)/x^2)*(exp(2*x)*(1750*x - 1000*x^2 + 28 0*x^3 - 38*x^4 + 2*x^5 - 1250) + exp(x)*(50*x - 50*x^2 + 268*x^3 - 402*x^4 + 180*x^5 - 32*x^6 + 2*x^7) - 50*x^3 + 1290*x^4 - 1506*x^5 + 600*x^6 - 10 0*x^7 + 6*x^8))/(5*x^3),x)
Output:
(exp(150*exp(2*x))*exp(-1002*x*exp(x))*exp(-50*x)*exp(x^6)*exp(1)*exp(-20* x*exp(2*x))*exp(2*x^4*exp(x))*exp(-40*x^3*exp(x))*exp(-(50*exp(x))/x)*exp( 300*x^2*exp(x))*exp(-20*x^5)*exp(150*x^4)*exp(-502*x^3)*exp(645*x^2)*exp(1 270*exp(x))*exp(x^2*exp(2*x))*exp(-(500*exp(2*x))/x)*exp((625*exp(2*x))/x^ 2))/5
\[ \int \frac {e^{\frac {x^2-50 x^3+645 x^4-502 x^5+150 x^6-20 x^7+x^8+e^{2 x} \left (625-500 x+150 x^2-20 x^3+x^4\right )+e^x \left (-50 x+1270 x^2-1002 x^3+300 x^4-40 x^5+2 x^6\right )}{x^2}} \left (-50 x^3+1290 x^4-1506 x^5+600 x^6-100 x^7+6 x^8+e^{2 x} \left (-1250+1750 x-1000 x^2+280 x^3-38 x^4+2 x^5\right )+e^x \left (50 x-50 x^2+268 x^3-402 x^4+180 x^5-32 x^6+2 x^7\right )\right )}{5 x^3} \, dx=\int \frac {\left (\left (2 x^{5}-38 x^{4}+280 x^{3}-1000 x^{2}+1750 x -1250\right ) \left ({\mathrm e}^{x}\right )^{2}+\left (2 x^{7}-32 x^{6}+180 x^{5}-402 x^{4}+268 x^{3}-50 x^{2}+50 x \right ) {\mathrm e}^{x}+6 x^{8}-100 x^{7}+600 x^{6}-1506 x^{5}+1290 x^{4}-50 x^{3}\right ) {\mathrm e}^{\frac {\left (x^{4}-20 x^{3}+150 x^{2}-500 x +625\right ) \left ({\mathrm e}^{x}\right )^{2}+\left (2 x^{6}-40 x^{5}+300 x^{4}-1002 x^{3}+1270 x^{2}-50 x \right ) {\mathrm e}^{x}+x^{8}-20 x^{7}+150 x^{6}-502 x^{5}+645 x^{4}-50 x^{3}+x^{2}}{x^{2}}}}{5 x^{3}}d x \] Input:
int(1/5*((2*x^5-38*x^4+280*x^3-1000*x^2+1750*x-1250)*exp(x)^2+(2*x^7-32*x^ 6+180*x^5-402*x^4+268*x^3-50*x^2+50*x)*exp(x)+6*x^8-100*x^7+600*x^6-1506*x ^5+1290*x^4-50*x^3)*exp(((x^4-20*x^3+150*x^2-500*x+625)*exp(x)^2+(2*x^6-40 *x^5+300*x^4-1002*x^3+1270*x^2-50*x)*exp(x)+x^8-20*x^7+150*x^6-502*x^5+645 *x^4-50*x^3+x^2)/x^2)/x^3,x)
Output:
int(1/5*((2*x^5-38*x^4+280*x^3-1000*x^2+1750*x-1250)*exp(x)^2+(2*x^7-32*x^ 6+180*x^5-402*x^4+268*x^3-50*x^2+50*x)*exp(x)+6*x^8-100*x^7+600*x^6-1506*x ^5+1290*x^4-50*x^3)*exp(((x^4-20*x^3+150*x^2-500*x+625)*exp(x)^2+(2*x^6-40 *x^5+300*x^4-1002*x^3+1270*x^2-50*x)*exp(x)+x^8-20*x^7+150*x^6-502*x^5+645 *x^4-50*x^3+x^2)/x^2)/x^3,x)