Integrand size = 148, antiderivative size = 30 \[ \int \frac {100 e^{\frac {3 (8+2 x)}{x^2}} x^2+e^{\frac {2 (8+2 x)}{x^2}} \left (400+50 x+25 x^2\right )}{-8 x^5+e^{\frac {3 (8+2 x)}{x^2}} \left (8 e^3 x^2-96 e^2 x^3+384 e x^4-512 x^5\right )+e^{\frac {2 (8+2 x)}{x^2}} \left (-24 e^2 x^3+192 e x^4-384 x^5\right )+e^{\frac {8+2 x}{x^2}} \left (24 e x^4-96 x^5\right )} \, dx=\frac {1}{16 \left (-x+\frac {1}{5} \left (e+x-e^{-\frac {2 (4+x)}{x^2}} x\right )\right )^2} \] Output:
1/4/(1/5*exp(1)-4/5*x-1/5*x/exp(2*(4+x)/x^2))/(4/5*exp(1)-16/5*x-4/5*x/exp (2*(4+x)/x^2))
Time = 0.98 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.57 \[ \int \frac {100 e^{\frac {3 (8+2 x)}{x^2}} x^2+e^{\frac {2 (8+2 x)}{x^2}} \left (400+50 x+25 x^2\right )}{-8 x^5+e^{\frac {3 (8+2 x)}{x^2}} \left (8 e^3 x^2-96 e^2 x^3+384 e x^4-512 x^5\right )+e^{\frac {2 (8+2 x)}{x^2}} \left (-24 e^2 x^3+192 e x^4-384 x^5\right )+e^{\frac {8+2 x}{x^2}} \left (24 e x^4-96 x^5\right )} \, dx=\frac {25 e^{\frac {4 (4+x)}{x^2}}}{16 \left (-e^{\frac {8+2 x+x^2}{x^2}}+x+4 e^{\frac {2 (4+x)}{x^2}} x\right )^2} \] Input:
Integrate[(100*E^((3*(8 + 2*x))/x^2)*x^2 + E^((2*(8 + 2*x))/x^2)*(400 + 50 *x + 25*x^2))/(-8*x^5 + E^((3*(8 + 2*x))/x^2)*(8*E^3*x^2 - 96*E^2*x^3 + 38 4*E*x^4 - 512*x^5) + E^((2*(8 + 2*x))/x^2)*(-24*E^2*x^3 + 192*E*x^4 - 384* x^5) + E^((8 + 2*x)/x^2)*(24*E*x^4 - 96*x^5)),x]
Output:
(25*E^((4*(4 + x))/x^2))/(16*(-E^((8 + 2*x + x^2)/x^2) + x + 4*E^((2*(4 + x))/x^2)*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.
| \(\displaystyle \int \frac {100 e^{\frac {3 (2 x+8)}{x^2}} x^2+e^{\frac {2 (2 x+8)}{x^2}} \left (25 x^2+50 x+400\right )}{-8 x^5+e^{\frac {2 x+8}{x^2}} \left (24 e x^4-96 x^5\right )+e^{\frac {3 (2 x+8)}{x^2}} \left (-512 x^5+384 e x^4-96 e^2 x^3+8 e^3 x^2\right )+e^{\frac {2 (2 x+8)}{x^2}} \left (-384 x^5+192 e x^4-24 e^2 x^3\right )} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {25 e^{\frac {4 (x+4)}{x^2}} \left (\left (4 e^{\frac {2 (x+4)}{x^2}}+1\right ) x^2+2 x+16\right )}{8 x^2 \left (-4 e^{\frac {2 (x+4)}{x^2}} x+e^{\frac {x^2+2 x+8}{x^2}}-x\right )^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {25}{8} \int \frac {e^{\frac {4 (x+4)}{x^2}} \left (\left (1+4 e^{\frac {2 (x+4)}{x^2}}\right ) x^2+2 x+16\right )}{x^2 \left (-4 e^{\frac {2 (x+4)}{x^2}} x-x+e^{\frac {x^2+2 x+8}{x^2}}\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {25}{8} \int \left (\frac {e^{\frac {4 (x+4)}{x^2}} \left (-\left ((8-e) x^2\right )-2 (32-e) x+16 e\right )}{(e-4 x) x^2 \left (-4 e^{\frac {2}{x}+\frac {8}{x^2}} x-x+e^{1+\frac {2}{x}+\frac {8}{x^2}}\right )^3}+\frac {4 e^{\frac {4 (x+4)}{x^2}}}{(e-4 x) \left (-4 e^{\frac {2}{x}+\frac {8}{x^2}} x-x+e^{1+\frac {2}{x}+\frac {8}{x^2}}\right )^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {25}{8} \left (\int \frac {e^{\frac {4 (x+4)}{x^2}+1}}{(e-4 x) \left (-4 e^{\frac {2}{x}+\frac {8}{x^2}} x-x+e^{1+\frac {2}{x}+\frac {8}{x^2}}\right )^3}dx+4 \int \frac {e^{\frac {4 (x+4)}{x^2}}}{(e-4 x) \left (-4 e^{\frac {2}{x}+\frac {8}{x^2}} x-x+e^{1+\frac {2}{x}+\frac {8}{x^2}}\right )^2}dx-16 \int \frac {e^{\frac {4 (x+4)}{x^2}}}{x^2 \left (4 e^{\frac {2}{x}+\frac {8}{x^2}} x+x-e^{1+\frac {2}{x}+\frac {8}{x^2}}\right )^3}dx-2 \int \frac {e^{\frac {4 (x+4)}{x^2}}}{x \left (4 e^{\frac {2}{x}+\frac {8}{x^2}} x+x-e^{1+\frac {2}{x}+\frac {8}{x^2}}\right )^3}dx\right )\) |
Input:
Int[(100*E^((3*(8 + 2*x))/x^2)*x^2 + E^((2*(8 + 2*x))/x^2)*(400 + 50*x + 2 5*x^2))/(-8*x^5 + E^((3*(8 + 2*x))/x^2)*(8*E^3*x^2 - 96*E^2*x^3 + 384*E*x^ 4 - 512*x^5) + E^((2*(8 + 2*x))/x^2)*(-24*E^2*x^3 + 192*E*x^4 - 384*x^5) + E^((8 + 2*x)/x^2)*(24*E*x^4 - 96*x^5)),x]
Output:
$Aborted
Time = 0.77 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.57
| method | result | size |
| norman | \(\frac {25 \,{\mathrm e}^{\frac {4 x +16}{x^{2}}}}{16 \left ({\mathrm e} \,{\mathrm e}^{\frac {2 x +8}{x^{2}}}-4 x \,{\mathrm e}^{\frac {2 x +8}{x^{2}}}-x \right )^{2}}\) | \(47\) |
| risch | \(\frac {25 \,{\mathrm e}^{\frac {4 x +16}{x^{2}}} x^{2}-\frac {25 x \,{\mathrm e}^{\frac {x^{2}+4 x +16}{x^{2}}}}{2}+\frac {25 \,{\mathrm e}^{\frac {2 x^{2}+4 x +16}{x^{2}}}}{16}}{\left ({\mathrm e}^{2}-8 x \,{\mathrm e}+16 x^{2}\right ) \left (4 x \,{\mathrm e}^{\frac {2 x +8}{x^{2}}}-{\mathrm e}^{\frac {x^{2}+2 x +8}{x^{2}}}+x \right )^{2}}\) | \(94\) |
| parallelrisch | \(\frac {25 \,{\mathrm e}^{\frac {4 x +16}{x^{2}}}}{16 \left ({\mathrm e}^{2} {\mathrm e}^{\frac {4 x +16}{x^{2}}}-8 \,{\mathrm e}^{\frac {4 x +16}{x^{2}}} {\mathrm e} x +16 \,{\mathrm e}^{\frac {4 x +16}{x^{2}}} x^{2}-2 \,{\mathrm e} \,{\mathrm e}^{\frac {2 x +8}{x^{2}}} x +8 x^{2} {\mathrm e}^{\frac {2 x +8}{x^{2}}}+x^{2}\right )}\) | \(96\) |
Input:
int((100*x^2*exp((2*x+8)/x^2)^3+(25*x^2+50*x+400)*exp((2*x+8)/x^2)^2)/((8* x^2*exp(1)^3-96*x^3*exp(1)^2+384*x^4*exp(1)-512*x^5)*exp((2*x+8)/x^2)^3+(- 24*x^3*exp(1)^2+192*x^4*exp(1)-384*x^5)*exp((2*x+8)/x^2)^2+(24*x^4*exp(1)- 96*x^5)*exp((2*x+8)/x^2)-8*x^5),x,method=_RETURNVERBOSE)
Output:
25/16*exp((2*x+8)/x^2)^2/(exp(1)*exp((2*x+8)/x^2)-4*x*exp((2*x+8)/x^2)-x)^ 2
Leaf count of result is larger than twice the leaf count of optimal. 62 vs. \(2 (23) = 46\).
Time = 0.11 (sec) , antiderivative size = 62, normalized size of antiderivative = 2.07 \[ \int \frac {100 e^{\frac {3 (8+2 x)}{x^2}} x^2+e^{\frac {2 (8+2 x)}{x^2}} \left (400+50 x+25 x^2\right )}{-8 x^5+e^{\frac {3 (8+2 x)}{x^2}} \left (8 e^3 x^2-96 e^2 x^3+384 e x^4-512 x^5\right )+e^{\frac {2 (8+2 x)}{x^2}} \left (-24 e^2 x^3+192 e x^4-384 x^5\right )+e^{\frac {8+2 x}{x^2}} \left (24 e x^4-96 x^5\right )} \, dx=\frac {25 \, e^{\left (\frac {4 \, {\left (x + 4\right )}}{x^{2}}\right )}}{16 \, {\left (x^{2} + {\left (16 \, x^{2} - 8 \, x e + e^{2}\right )} e^{\left (\frac {4 \, {\left (x + 4\right )}}{x^{2}}\right )} + 2 \, {\left (4 \, x^{2} - x e\right )} e^{\left (\frac {2 \, {\left (x + 4\right )}}{x^{2}}\right )}\right )}} \] Input:
integrate((100*x^2*exp((2*x+8)/x^2)^3+(25*x^2+50*x+400)*exp((2*x+8)/x^2)^2 )/((8*x^2*exp(1)^3-96*x^3*exp(1)^2+384*x^4*exp(1)-512*x^5)*exp((2*x+8)/x^2 )^3+(-24*x^3*exp(1)^2+192*x^4*exp(1)-384*x^5)*exp((2*x+8)/x^2)^2+(24*x^4*e xp(1)-96*x^5)*exp((2*x+8)/x^2)-8*x^5),x, algorithm="fricas")
Output:
25/16*e^(4*(x + 4)/x^2)/(x^2 + (16*x^2 - 8*x*e + e^2)*e^(4*(x + 4)/x^2) + 2*(4*x^2 - x*e)*e^(2*(x + 4)/x^2))
Leaf count of result is larger than twice the leaf count of optimal. 150 vs. \(2 (53) = 106\).
Time = 0.30 (sec) , antiderivative size = 150, normalized size of antiderivative = 5.00 \[ \int \frac {100 e^{\frac {3 (8+2 x)}{x^2}} x^2+e^{\frac {2 (8+2 x)}{x^2}} \left (400+50 x+25 x^2\right )}{-8 x^5+e^{\frac {3 (8+2 x)}{x^2}} \left (8 e^3 x^2-96 e^2 x^3+384 e x^4-512 x^5\right )+e^{\frac {2 (8+2 x)}{x^2}} \left (-24 e^2 x^3+192 e x^4-384 x^5\right )+e^{\frac {8+2 x}{x^2}} \left (24 e x^4-96 x^5\right )} \, dx=\frac {- 25 x^{2} + \left (- 200 x^{2} + 50 e x\right ) e^{\frac {2 x + 8}{x^{2}}}}{256 x^{4} - 128 e x^{3} + 16 x^{2} e^{2} + \left (2048 x^{4} - 1536 e x^{3} + 384 x^{2} e^{2} - 32 x e^{3}\right ) e^{\frac {2 x + 8}{x^{2}}} + \left (4096 x^{4} - 4096 e x^{3} + 1536 x^{2} e^{2} - 256 x e^{3} + 16 e^{4}\right ) e^{\frac {2 \cdot \left (2 x + 8\right )}{x^{2}}}} + \frac {25}{256 x^{2} - 128 e x + 16 e^{2}} \] Input:
integrate((100*x**2*exp((2*x+8)/x**2)**3+(25*x**2+50*x+400)*exp((2*x+8)/x* *2)**2)/((8*x**2*exp(1)**3-96*x**3*exp(1)**2+384*x**4*exp(1)-512*x**5)*exp ((2*x+8)/x**2)**3+(-24*x**3*exp(1)**2+192*x**4*exp(1)-384*x**5)*exp((2*x+8 )/x**2)**2+(24*x**4*exp(1)-96*x**5)*exp((2*x+8)/x**2)-8*x**5),x)
Output:
(-25*x**2 + (-200*x**2 + 50*E*x)*exp((2*x + 8)/x**2))/(256*x**4 - 128*E*x* *3 + 16*x**2*exp(2) + (2048*x**4 - 1536*E*x**3 + 384*x**2*exp(2) - 32*x*ex p(3))*exp((2*x + 8)/x**2) + (4096*x**4 - 4096*E*x**3 + 1536*x**2*exp(2) - 256*x*exp(3) + 16*exp(4))*exp(2*(2*x + 8)/x**2)) + 25/(256*x**2 - 128*E*x + 16*exp(2))
Leaf count of result is larger than twice the leaf count of optimal. 71 vs. \(2 (23) = 46\).
Time = 0.15 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.37 \[ \int \frac {100 e^{\frac {3 (8+2 x)}{x^2}} x^2+e^{\frac {2 (8+2 x)}{x^2}} \left (400+50 x+25 x^2\right )}{-8 x^5+e^{\frac {3 (8+2 x)}{x^2}} \left (8 e^3 x^2-96 e^2 x^3+384 e x^4-512 x^5\right )+e^{\frac {2 (8+2 x)}{x^2}} \left (-24 e^2 x^3+192 e x^4-384 x^5\right )+e^{\frac {8+2 x}{x^2}} \left (24 e x^4-96 x^5\right )} \, dx=\frac {25 \, e^{\left (\frac {4}{x} + \frac {16}{x^{2}}\right )}}{16 \, {\left (x^{2} + {\left (16 \, x^{2} - 8 \, x e + e^{2}\right )} e^{\left (\frac {4}{x} + \frac {16}{x^{2}}\right )} + 2 \, {\left (4 \, x^{2} - x e\right )} e^{\left (\frac {2}{x} + \frac {8}{x^{2}}\right )}\right )}} \] Input:
integrate((100*x^2*exp((2*x+8)/x^2)^3+(25*x^2+50*x+400)*exp((2*x+8)/x^2)^2 )/((8*x^2*exp(1)^3-96*x^3*exp(1)^2+384*x^4*exp(1)-512*x^5)*exp((2*x+8)/x^2 )^3+(-24*x^3*exp(1)^2+192*x^4*exp(1)-384*x^5)*exp((2*x+8)/x^2)^2+(24*x^4*e xp(1)-96*x^5)*exp((2*x+8)/x^2)-8*x^5),x, algorithm="maxima")
Output:
25/16*e^(4/x + 16/x^2)/(x^2 + (16*x^2 - 8*x*e + e^2)*e^(4/x + 16/x^2) + 2* (4*x^2 - x*e)*e^(2/x + 8/x^2))
Leaf count of result is larger than twice the leaf count of optimal. 28878 vs. \(2 (23) = 46\).
Time = 0.44 (sec) , antiderivative size = 28878, normalized size of antiderivative = 962.60 \[ \int \frac {100 e^{\frac {3 (8+2 x)}{x^2}} x^2+e^{\frac {2 (8+2 x)}{x^2}} \left (400+50 x+25 x^2\right )}{-8 x^5+e^{\frac {3 (8+2 x)}{x^2}} \left (8 e^3 x^2-96 e^2 x^3+384 e x^4-512 x^5\right )+e^{\frac {2 (8+2 x)}{x^2}} \left (-24 e^2 x^3+192 e x^4-384 x^5\right )+e^{\frac {8+2 x}{x^2}} \left (24 e x^4-96 x^5\right )} \, dx=\text {Too large to display} \] Input:
integrate((100*x^2*exp((2*x+8)/x^2)^3+(25*x^2+50*x+400)*exp((2*x+8)/x^2)^2 )/((8*x^2*exp(1)^3-96*x^3*exp(1)^2+384*x^4*exp(1)-512*x^5)*exp((2*x+8)/x^2 )^3+(-24*x^3*exp(1)^2+192*x^4*exp(1)-384*x^5)*exp((2*x+8)/x^2)^2+(24*x^4*e xp(1)-96*x^5)*exp((2*x+8)/x^2)-8*x^5),x, algorithm="giac")
Output:
25/16*(65536*x^14*e^(22*(x + 4)/x^2) + 131072*x^14*e^(20*(x + 4)/x^2) + 11 4688*x^14*e^(18*(x + 4)/x^2) + 57344*x^14*e^(16*(x + 4)/x^2) + 17920*x^14* e^(14*(x + 4)/x^2) + 3584*x^14*e^(12*(x + 4)/x^2) + 448*x^14*e^(10*(x + 4) /x^2) + 32*x^14*e^(8*(x + 4)/x^2) + x^14*e^(6*(x + 4)/x^2) - 8192*x^13*e^( (x^2 + 3*x + 12)/x^2 + 17*(x + 4)/x^2) - 12288*x^13*e^((x^2 + 3*x + 12)/x^ 2 + 15*(x + 4)/x^2) - 7680*x^13*e^((x^2 + 3*x + 12)/x^2 + 13*(x + 4)/x^2) - 2560*x^13*e^((x^2 + 3*x + 12)/x^2 + 11*(x + 4)/x^2) - 480*x^13*e^((x^2 + 3*x + 12)/x^2 + 9*(x + 4)/x^2) - 48*x^13*e^((x^2 + 3*x + 12)/x^2 + 7*(x + 4)/x^2) - 2*x^13*e^((x^2 + 3*x + 12)/x^2 + 5*(x + 4)/x^2) - 32768*x^13*e^ ((x^2 + 2*x + 8)/x^2 + 20*(x + 4)/x^2) - 49152*x^13*e^((x^2 + 2*x + 8)/x^2 + 18*(x + 4)/x^2) - 30720*x^13*e^((x^2 + 2*x + 8)/x^2 + 16*(x + 4)/x^2) - 10240*x^13*e^((x^2 + 2*x + 8)/x^2 + 14*(x + 4)/x^2) - 1920*x^13*e^((x^2 + 2*x + 8)/x^2 + 12*(x + 4)/x^2) - 192*x^13*e^((x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) - 8*x^13*e^((x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) + 196608*x^13*e ^(20*(x + 4)/x^2) + 344064*x^13*e^(18*(x + 4)/x^2) + 258048*x^13*e^(16*(x + 4)/x^2) + 107520*x^13*e^(14*(x + 4)/x^2) + 26880*x^13*e^(12*(x + 4)/x^2) + 4032*x^13*e^(10*(x + 4)/x^2) + 336*x^13*e^(8*(x + 4)/x^2) + 12*x^13*e^( 6*(x + 4)/x^2) + 1024*x^12*e^(2*(x^2 + 3*x + 12)/x^2 + 14*(x + 4)/x^2) + 1 280*x^12*e^(2*(x^2 + 3*x + 12)/x^2 + 12*(x + 4)/x^2) + 640*x^12*e^(2*(x^2 + 3*x + 12)/x^2 + 10*(x + 4)/x^2) + 160*x^12*e^(2*(x^2 + 3*x + 12)/x^2 ...
Timed out. \[ \int \frac {100 e^{\frac {3 (8+2 x)}{x^2}} x^2+e^{\frac {2 (8+2 x)}{x^2}} \left (400+50 x+25 x^2\right )}{-8 x^5+e^{\frac {3 (8+2 x)}{x^2}} \left (8 e^3 x^2-96 e^2 x^3+384 e x^4-512 x^5\right )+e^{\frac {2 (8+2 x)}{x^2}} \left (-24 e^2 x^3+192 e x^4-384 x^5\right )+e^{\frac {8+2 x}{x^2}} \left (24 e x^4-96 x^5\right )} \, dx=\int -\frac {100\,x^2\,{\mathrm {e}}^{\frac {3\,\left (2\,x+8\right )}{x^2}}+{\mathrm {e}}^{\frac {2\,\left (2\,x+8\right )}{x^2}}\,\left (25\,x^2+50\,x+400\right )}{{\mathrm {e}}^{\frac {2\,\left (2\,x+8\right )}{x^2}}\,\left (384\,x^5-192\,\mathrm {e}\,x^4+24\,{\mathrm {e}}^2\,x^3\right )-{\mathrm {e}}^{\frac {2\,x+8}{x^2}}\,\left (24\,x^4\,\mathrm {e}-96\,x^5\right )-{\mathrm {e}}^{\frac {3\,\left (2\,x+8\right )}{x^2}}\,\left (-512\,x^5+384\,\mathrm {e}\,x^4-96\,{\mathrm {e}}^2\,x^3+8\,{\mathrm {e}}^3\,x^2\right )+8\,x^5} \,d x \] Input:
int(-(100*x^2*exp((3*(2*x + 8))/x^2) + exp((2*(2*x + 8))/x^2)*(50*x + 25*x ^2 + 400))/(exp((2*(2*x + 8))/x^2)*(24*x^3*exp(2) - 192*x^4*exp(1) + 384*x ^5) - exp((2*x + 8)/x^2)*(24*x^4*exp(1) - 96*x^5) - exp((3*(2*x + 8))/x^2) *(8*x^2*exp(3) - 96*x^3*exp(2) + 384*x^4*exp(1) - 512*x^5) + 8*x^5),x)
Output:
int(-(100*x^2*exp((3*(2*x + 8))/x^2) + exp((2*(2*x + 8))/x^2)*(50*x + 25*x ^2 + 400))/(exp((2*(2*x + 8))/x^2)*(24*x^3*exp(2) - 192*x^4*exp(1) + 384*x ^5) - exp((2*x + 8)/x^2)*(24*x^4*exp(1) - 96*x^5) - exp((3*(2*x + 8))/x^2) *(8*x^2*exp(3) - 96*x^3*exp(2) + 384*x^4*exp(1) - 512*x^5) + 8*x^5), x)
\[ \int \frac {100 e^{\frac {3 (8+2 x)}{x^2}} x^2+e^{\frac {2 (8+2 x)}{x^2}} \left (400+50 x+25 x^2\right )}{-8 x^5+e^{\frac {3 (8+2 x)}{x^2}} \left (8 e^3 x^2-96 e^2 x^3+384 e x^4-512 x^5\right )+e^{\frac {2 (8+2 x)}{x^2}} \left (-24 e^2 x^3+192 e x^4-384 x^5\right )+e^{\frac {8+2 x}{x^2}} \left (24 e x^4-96 x^5\right )} \, dx=\int \frac {100 x^{2} \left ({\mathrm e}^{\frac {2 x +8}{x^{2}}}\right )^{3}+\left (25 x^{2}+50 x +400\right ) \left ({\mathrm e}^{\frac {2 x +8}{x^{2}}}\right )^{2}}{\left (8 x^{2} \left ({\mathrm e}\right )^{3}-96 x^{3} \left ({\mathrm e}\right )^{2}+384 x^{4} {\mathrm e}-512 x^{5}\right ) \left ({\mathrm e}^{\frac {2 x +8}{x^{2}}}\right )^{3}+\left (-24 x^{3} \left ({\mathrm e}\right )^{2}+192 x^{4} {\mathrm e}-384 x^{5}\right ) \left ({\mathrm e}^{\frac {2 x +8}{x^{2}}}\right )^{2}+\left (24 x^{4} {\mathrm e}-96 x^{5}\right ) {\mathrm e}^{\frac {2 x +8}{x^{2}}}-8 x^{5}}d x \] Input:
int((100*x^2*exp((2*x+8)/x^2)^3+(25*x^2+50*x+400)*exp((2*x+8)/x^2)^2)/((8* x^2*exp(1)^3-96*x^3*exp(1)^2+384*x^4*exp(1)-512*x^5)*exp((2*x+8)/x^2)^3+(- 24*x^3*exp(1)^2+192*x^4*exp(1)-384*x^5)*exp((2*x+8)/x^2)^2+(24*x^4*exp(1)- 96*x^5)*exp((2*x+8)/x^2)-8*x^5),x)
Output:
int((100*x^2*exp((2*x+8)/x^2)^3+(25*x^2+50*x+400)*exp((2*x+8)/x^2)^2)/((8* x^2*exp(1)^3-96*x^3*exp(1)^2+384*x^4*exp(1)-512*x^5)*exp((2*x+8)/x^2)^3+(- 24*x^3*exp(1)^2+192*x^4*exp(1)-384*x^5)*exp((2*x+8)/x^2)^2+(24*x^4*exp(1)- 96*x^5)*exp((2*x+8)/x^2)-8*x^5),x)