Integrand size = 163, antiderivative size = 24 \[ \int \frac {e^{\frac {2 \left (189 x+198 x^2+111 x^3+30 x^4+3 x^5+e^8 \left (432 x+288 x^2+48 x^3\right )+e^4 \left (216 x+432 x^2+192 x^3+24 x^4\right )\right )}{9+6 x+x^2}} \left (1134+1998 x+1998 x^2+942 x^3+210 x^4+18 x^5+e^8 \left (2592+2592 x+864 x^2+96 x^3\right )+e^4 \left (1296+4752 x+3456 x^2+960 x^3+96 x^4\right )\right )}{27+27 x+9 x^2+x^3} \, dx=e^{6 x \left (6+\left (1+4 e^4+x+\frac {x}{3+x}\right )^2\right )} \] Output:
exp(3*x*(6+(x+x/(3+x)+1+4*exp(4))^2))^2
Leaf count is larger than twice the leaf count of optimal. \(56\) vs. \(2(24)=48\).
Time = 0.07 (sec) , antiderivative size = 56, normalized size of antiderivative = 2.33 \[ \int \frac {e^{\frac {2 \left (189 x+198 x^2+111 x^3+30 x^4+3 x^5+e^8 \left (432 x+288 x^2+48 x^3\right )+e^4 \left (216 x+432 x^2+192 x^3+24 x^4\right )\right )}{9+6 x+x^2}} \left (1134+1998 x+1998 x^2+942 x^3+210 x^4+18 x^5+e^8 \left (2592+2592 x+864 x^2+96 x^3\right )+e^4 \left (1296+4752 x+3456 x^2+960 x^3+96 x^4\right )\right )}{27+27 x+9 x^2+x^3} \, dx=e^{\frac {6 x \left (63+66 x+37 x^2+10 x^3+x^4+16 e^8 (3+x)^2+8 e^4 \left (9+18 x+8 x^2+x^3\right )\right )}{(3+x)^2}} \] Input:
Integrate[(E^((2*(189*x + 198*x^2 + 111*x^3 + 30*x^4 + 3*x^5 + E^8*(432*x + 288*x^2 + 48*x^3) + E^4*(216*x + 432*x^2 + 192*x^3 + 24*x^4)))/(9 + 6*x + x^2))*(1134 + 1998*x + 1998*x^2 + 942*x^3 + 210*x^4 + 18*x^5 + E^8*(2592 + 2592*x + 864*x^2 + 96*x^3) + E^4*(1296 + 4752*x + 3456*x^2 + 960*x^3 + 96*x^4)))/(27 + 27*x + 9*x^2 + x^3),x]
Output:
E^((6*x*(63 + 66*x + 37*x^2 + 10*x^3 + x^4 + 16*E^8*(3 + x)^2 + 8*E^4*(9 + 18*x + 8*x^2 + x^3)))/(3 + 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.
| \(\displaystyle \int \frac {\left (18 x^5+210 x^4+942 x^3+1998 x^2+e^8 \left (96 x^3+864 x^2+2592 x+2592\right )+e^4 \left (96 x^4+960 x^3+3456 x^2+4752 x+1296\right )+1998 x+1134\right ) \exp \left (\frac {2 \left (3 x^5+30 x^4+111 x^3+198 x^2+e^8 \left (48 x^3+288 x^2+432 x\right )+e^4 \left (24 x^4+192 x^3+432 x^2+216 x\right )+189 x\right )}{x^2+6 x+9}\right )}{x^3+9 x^2+27 x+27} \, dx\) |
| \(\Big \downarrow \) 2007 |
| \(\displaystyle \int \frac {\left (18 x^5+210 x^4+942 x^3+1998 x^2+e^8 \left (96 x^3+864 x^2+2592 x+2592\right )+e^4 \left (96 x^4+960 x^3+3456 x^2+4752 x+1296\right )+1998 x+1134\right ) \exp \left (\frac {2 \left (3 x^5+30 x^4+111 x^3+198 x^2+e^8 \left (48 x^3+288 x^2+432 x\right )+e^4 \left (24 x^4+192 x^3+432 x^2+216 x\right )+189 x\right )}{x^2+6 x+9}\right )}{(x+3)^3}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {\left (18 x^5+210 x^4+942 x^3+1998 x^2+e^8 \left (96 x^3+864 x^2+2592 x+2592\right )+e^4 \left (96 x^4+960 x^3+3456 x^2+4752 x+1296\right )+1998 x+1134\right ) \exp \left (\frac {6 x \left (x^4+2 \left (5+4 e^4\right ) x^3+\left (37+64 e^4+16 e^8\right ) x^2+6 \left (11+24 e^4+16 e^8\right ) x+9 \left (7+8 e^4+16 e^8\right )\right )}{x^2+6 x+9}\right )}{(x+3)^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (18 x^2 \exp \left (\frac {6 x \left (x^4+2 \left (5+4 e^4\right ) x^3+\left (37+64 e^4+16 e^8\right ) x^2+6 \left (11+24 e^4+16 e^8\right ) x+9 \left (7+8 e^4+16 e^8\right )\right )}{x^2+6 x+9}\right )+48 \left (1+2 e^4\right ) x \exp \left (\frac {6 x \left (x^4+2 \left (5+4 e^4\right ) x^3+\left (37+64 e^4+16 e^8\right ) x^2+6 \left (11+24 e^4+16 e^8\right ) x+9 \left (7+8 e^4+16 e^8\right )\right )}{x^2+6 x+9}\right )-\frac {54 \left (8 e^4-1\right ) \exp \left (\frac {6 x \left (x^4+2 \left (5+4 e^4\right ) x^3+\left (37+64 e^4+16 e^8\right ) x^2+6 \left (11+24 e^4+16 e^8\right ) x+9 \left (7+8 e^4+16 e^8\right )\right )}{x^2+6 x+9}\right )}{(x+3)^2}+\frac {324 \exp \left (\frac {6 x \left (x^4+2 \left (5+4 e^4\right ) x^3+\left (37+64 e^4+16 e^8\right ) x^2+6 \left (11+24 e^4+16 e^8\right ) x+9 \left (7+8 e^4+16 e^8\right )\right )}{x^2+6 x+9}\right )}{(x+3)^3}+24 \left (1+2 e^4\right )^2 \exp \left (\frac {6 x \left (x^4+2 \left (5+4 e^4\right ) x^3+\left (37+64 e^4+16 e^8\right ) x^2+6 \left (11+24 e^4+16 e^8\right ) x+9 \left (7+8 e^4+16 e^8\right )\right )}{x^2+6 x+9}\right )\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 24 \left (1+2 e^4\right )^2 \int \exp \left (\frac {6 x \left (x^4+2 \left (5+4 e^4\right ) x^3+\left (37+64 e^4+16 e^8\right ) x^2+6 \left (11+24 e^4+16 e^8\right ) x+9 \left (7+8 e^4+16 e^8\right )\right )}{x^2+6 x+9}\right )dx+48 \left (1+2 e^4\right ) \int \exp \left (\frac {6 x \left (x^4+2 \left (5+4 e^4\right ) x^3+\left (37+64 e^4+16 e^8\right ) x^2+6 \left (11+24 e^4+16 e^8\right ) x+9 \left (7+8 e^4+16 e^8\right )\right )}{x^2+6 x+9}\right ) xdx+18 \int \exp \left (\frac {6 x \left (x^4+2 \left (5+4 e^4\right ) x^3+\left (37+64 e^4+16 e^8\right ) x^2+6 \left (11+24 e^4+16 e^8\right ) x+9 \left (7+8 e^4+16 e^8\right )\right )}{x^2+6 x+9}\right ) x^2dx+324 \int \frac {\exp \left (\frac {6 x \left (x^4+2 \left (5+4 e^4\right ) x^3+\left (37+64 e^4+16 e^8\right ) x^2+6 \left (11+24 e^4+16 e^8\right ) x+9 \left (7+8 e^4+16 e^8\right )\right )}{x^2+6 x+9}\right )}{(x+3)^3}dx+54 \left (1-8 e^4\right ) \int \frac {\exp \left (\frac {6 x \left (x^4+2 \left (5+4 e^4\right ) x^3+\left (37+64 e^4+16 e^8\right ) x^2+6 \left (11+24 e^4+16 e^8\right ) x+9 \left (7+8 e^4+16 e^8\right )\right )}{x^2+6 x+9}\right )}{(x+3)^2}dx\) |
Input:
Int[(E^((2*(189*x + 198*x^2 + 111*x^3 + 30*x^4 + 3*x^5 + E^8*(432*x + 288* x^2 + 48*x^3) + E^4*(216*x + 432*x^2 + 192*x^3 + 24*x^4)))/(9 + 6*x + x^2) )*(1134 + 1998*x + 1998*x^2 + 942*x^3 + 210*x^4 + 18*x^5 + E^8*(2592 + 259 2*x + 864*x^2 + 96*x^3) + E^4*(1296 + 4752*x + 3456*x^2 + 960*x^3 + 96*x^4 )))/(27 + 27*x + 9*x^2 + x^3),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(66\) vs. \(2(24)=48\).
Time = 163.05 (sec) , antiderivative size = 67, normalized size of antiderivative = 2.79
| method | result | size |
| risch | \({\mathrm e}^{\frac {6 x \left (8 x^{3} {\mathrm e}^{4}+x^{4}+64 x^{2} {\mathrm e}^{4}+16 x^{2} {\mathrm e}^{8}+10 x^{3}+144 x \,{\mathrm e}^{4}+96 x \,{\mathrm e}^{8}+37 x^{2}+72 \,{\mathrm e}^{4}+144 \,{\mathrm e}^{8}+66 x +63\right )}{\left (3+x \right )^{2}}}\) | \(67\) |
| gosper | \({\mathrm e}^{\frac {6 x \left (8 x^{3} {\mathrm e}^{4}+x^{4}+64 x^{2} {\mathrm e}^{4}+16 x^{2} {\mathrm e}^{8}+10 x^{3}+144 x \,{\mathrm e}^{4}+96 x \,{\mathrm e}^{8}+37 x^{2}+72 \,{\mathrm e}^{4}+144 \,{\mathrm e}^{8}+66 x +63\right )}{x^{2}+6 x +9}}\) | \(80\) |
| parallelrisch | \({\mathrm e}^{\frac {2 \left (48 x^{3}+288 x^{2}+432 x \right ) {\mathrm e}^{8}+2 \left (24 x^{4}+192 x^{3}+432 x^{2}+216 x \right ) {\mathrm e}^{4}+6 x^{5}+60 x^{4}+222 x^{3}+396 x^{2}+378 x}{x^{2}+6 x +9}}\) | \(80\) |
| norman | \(\frac {x^{2} {\mathrm e}^{\frac {2 \left (48 x^{3}+288 x^{2}+432 x \right ) {\mathrm e}^{8}+2 \left (24 x^{4}+192 x^{3}+432 x^{2}+216 x \right ) {\mathrm e}^{4}+6 x^{5}+60 x^{4}+222 x^{3}+396 x^{2}+378 x}{x^{2}+6 x +9}}+9 \,{\mathrm e}^{\frac {2 \left (48 x^{3}+288 x^{2}+432 x \right ) {\mathrm e}^{8}+2 \left (24 x^{4}+192 x^{3}+432 x^{2}+216 x \right ) {\mathrm e}^{4}+6 x^{5}+60 x^{4}+222 x^{3}+396 x^{2}+378 x}{x^{2}+6 x +9}}+6 x \,{\mathrm e}^{\frac {2 \left (48 x^{3}+288 x^{2}+432 x \right ) {\mathrm e}^{8}+2 \left (24 x^{4}+192 x^{3}+432 x^{2}+216 x \right ) {\mathrm e}^{4}+6 x^{5}+60 x^{4}+222 x^{3}+396 x^{2}+378 x}{x^{2}+6 x +9}}}{\left (3+x \right )^{2}}\) | \(254\) |
Input:
int(((96*x^3+864*x^2+2592*x+2592)*exp(4)^2+(96*x^4+960*x^3+3456*x^2+4752*x +1296)*exp(4)+18*x^5+210*x^4+942*x^3+1998*x^2+1998*x+1134)*exp(((48*x^3+28 8*x^2+432*x)*exp(4)^2+(24*x^4+192*x^3+432*x^2+216*x)*exp(4)+3*x^5+30*x^4+1 11*x^3+198*x^2+189*x)/(x^2+6*x+9))^2/(x^3+9*x^2+27*x+27),x,method=_RETURNV ERBOSE)
Output:
exp(6*x*(8*x^3*exp(4)+x^4+64*x^2*exp(4)+16*x^2*exp(8)+10*x^3+144*x*exp(4)+ 96*x*exp(8)+37*x^2+72*exp(4)+144*exp(8)+66*x+63)/(3+x)^2)
Leaf count of result is larger than twice the leaf count of optimal. 72 vs. \(2 (22) = 44\).
Time = 0.07 (sec) , antiderivative size = 72, normalized size of antiderivative = 3.00 \[ \int \frac {e^{\frac {2 \left (189 x+198 x^2+111 x^3+30 x^4+3 x^5+e^8 \left (432 x+288 x^2+48 x^3\right )+e^4 \left (216 x+432 x^2+192 x^3+24 x^4\right )\right )}{9+6 x+x^2}} \left (1134+1998 x+1998 x^2+942 x^3+210 x^4+18 x^5+e^8 \left (2592+2592 x+864 x^2+96 x^3\right )+e^4 \left (1296+4752 x+3456 x^2+960 x^3+96 x^4\right )\right )}{27+27 x+9 x^2+x^3} \, dx=e^{\left (\frac {6 \, {\left (x^{5} + 10 \, x^{4} + 37 \, x^{3} + 66 \, x^{2} + 16 \, {\left (x^{3} + 6 \, x^{2} + 9 \, x\right )} e^{8} + 8 \, {\left (x^{4} + 8 \, x^{3} + 18 \, x^{2} + 9 \, x\right )} e^{4} + 63 \, x\right )}}{x^{2} + 6 \, x + 9}\right )} \] Input:
integrate(((96*x^3+864*x^2+2592*x+2592)*exp(4)^2+(96*x^4+960*x^3+3456*x^2+ 4752*x+1296)*exp(4)+18*x^5+210*x^4+942*x^3+1998*x^2+1998*x+1134)*exp(((48* x^3+288*x^2+432*x)*exp(4)^2+(24*x^4+192*x^3+432*x^2+216*x)*exp(4)+3*x^5+30 *x^4+111*x^3+198*x^2+189*x)/(x^2+6*x+9))^2/(x^3+9*x^2+27*x+27),x, algorith m="fricas")
Output:
e^(6*(x^5 + 10*x^4 + 37*x^3 + 66*x^2 + 16*(x^3 + 6*x^2 + 9*x)*e^8 + 8*(x^4 + 8*x^3 + 18*x^2 + 9*x)*e^4 + 63*x)/(x^2 + 6*x + 9))
Leaf count of result is larger than twice the leaf count of optimal. 75 vs. \(2 (20) = 40\).
Time = 0.28 (sec) , antiderivative size = 75, normalized size of antiderivative = 3.12 \[ \int \frac {e^{\frac {2 \left (189 x+198 x^2+111 x^3+30 x^4+3 x^5+e^8 \left (432 x+288 x^2+48 x^3\right )+e^4 \left (216 x+432 x^2+192 x^3+24 x^4\right )\right )}{9+6 x+x^2}} \left (1134+1998 x+1998 x^2+942 x^3+210 x^4+18 x^5+e^8 \left (2592+2592 x+864 x^2+96 x^3\right )+e^4 \left (1296+4752 x+3456 x^2+960 x^3+96 x^4\right )\right )}{27+27 x+9 x^2+x^3} \, dx=e^{\frac {2 \cdot \left (3 x^{5} + 30 x^{4} + 111 x^{3} + 198 x^{2} + 189 x + \left (48 x^{3} + 288 x^{2} + 432 x\right ) e^{8} + \left (24 x^{4} + 192 x^{3} + 432 x^{2} + 216 x\right ) e^{4}\right )}{x^{2} + 6 x + 9}} \] Input:
integrate(((96*x**3+864*x**2+2592*x+2592)*exp(4)**2+(96*x**4+960*x**3+3456 *x**2+4752*x+1296)*exp(4)+18*x**5+210*x**4+942*x**3+1998*x**2+1998*x+1134) *exp(((48*x**3+288*x**2+432*x)*exp(4)**2+(24*x**4+192*x**3+432*x**2+216*x) *exp(4)+3*x**5+30*x**4+111*x**3+198*x**2+189*x)/(x**2+6*x+9))**2/(x**3+9*x **2+27*x+27),x)
Output:
exp(2*(3*x**5 + 30*x**4 + 111*x**3 + 198*x**2 + 189*x + (48*x**3 + 288*x** 2 + 432*x)*exp(8) + (24*x**4 + 192*x**3 + 432*x**2 + 216*x)*exp(4))/(x**2 + 6*x + 9))
Leaf count of result is larger than twice the leaf count of optimal. 65 vs. \(2 (22) = 44\).
Time = 0.68 (sec) , antiderivative size = 65, normalized size of antiderivative = 2.71 \[ \int \frac {e^{\frac {2 \left (189 x+198 x^2+111 x^3+30 x^4+3 x^5+e^8 \left (432 x+288 x^2+48 x^3\right )+e^4 \left (216 x+432 x^2+192 x^3+24 x^4\right )\right )}{9+6 x+x^2}} \left (1134+1998 x+1998 x^2+942 x^3+210 x^4+18 x^5+e^8 \left (2592+2592 x+864 x^2+96 x^3\right )+e^4 \left (1296+4752 x+3456 x^2+960 x^3+96 x^4\right )\right )}{27+27 x+9 x^2+x^3} \, dx=e^{\left (6 \, x^{3} + 48 \, x^{2} e^{4} + 24 \, x^{2} + 96 \, x e^{8} + 96 \, x e^{4} + 24 \, x + \frac {432 \, e^{4}}{x + 3} - \frac {162}{x^{2} + 6 \, x + 9} - \frac {54}{x + 3} - 144 \, e^{4} + 36\right )} \] Input:
integrate(((96*x^3+864*x^2+2592*x+2592)*exp(4)^2+(96*x^4+960*x^3+3456*x^2+ 4752*x+1296)*exp(4)+18*x^5+210*x^4+942*x^3+1998*x^2+1998*x+1134)*exp(((48* x^3+288*x^2+432*x)*exp(4)^2+(24*x^4+192*x^3+432*x^2+216*x)*exp(4)+3*x^5+30 *x^4+111*x^3+198*x^2+189*x)/(x^2+6*x+9))^2/(x^3+9*x^2+27*x+27),x, algorith m="maxima")
Output:
e^(6*x^3 + 48*x^2*e^4 + 24*x^2 + 96*x*e^8 + 96*x*e^4 + 24*x + 432*e^4/(x + 3) - 162/(x^2 + 6*x + 9) - 54/(x + 3) - 144*e^4 + 36)
Leaf count of result is larger than twice the leaf count of optimal. 80 vs. \(2 (22) = 44\).
Time = 0.39 (sec) , antiderivative size = 80, normalized size of antiderivative = 3.33 \[ \int \frac {e^{\frac {2 \left (189 x+198 x^2+111 x^3+30 x^4+3 x^5+e^8 \left (432 x+288 x^2+48 x^3\right )+e^4 \left (216 x+432 x^2+192 x^3+24 x^4\right )\right )}{9+6 x+x^2}} \left (1134+1998 x+1998 x^2+942 x^3+210 x^4+18 x^5+e^8 \left (2592+2592 x+864 x^2+96 x^3\right )+e^4 \left (1296+4752 x+3456 x^2+960 x^3+96 x^4\right )\right )}{27+27 x+9 x^2+x^3} \, dx=e^{\left (\frac {6 \, {\left (x^{5} + 8 \, x^{4} e^{4} + 10 \, x^{4} + 16 \, x^{3} e^{8} + 64 \, x^{3} e^{4} + 37 \, x^{3} + 96 \, x^{2} e^{8} + 144 \, x^{2} e^{4} + 66 \, x^{2} + 144 \, x e^{8} + 72 \, x e^{4} + 63 \, x\right )}}{x^{2} + 6 \, x + 9}\right )} \] Input:
integrate(((96*x^3+864*x^2+2592*x+2592)*exp(4)^2+(96*x^4+960*x^3+3456*x^2+ 4752*x+1296)*exp(4)+18*x^5+210*x^4+942*x^3+1998*x^2+1998*x+1134)*exp(((48* x^3+288*x^2+432*x)*exp(4)^2+(24*x^4+192*x^3+432*x^2+216*x)*exp(4)+3*x^5+30 *x^4+111*x^3+198*x^2+189*x)/(x^2+6*x+9))^2/(x^3+9*x^2+27*x+27),x, algorith m="giac")
Output:
e^(6*(x^5 + 8*x^4*e^4 + 10*x^4 + 16*x^3*e^8 + 64*x^3*e^4 + 37*x^3 + 96*x^2 *e^8 + 144*x^2*e^4 + 66*x^2 + 144*x*e^8 + 72*x*e^4 + 63*x)/(x^2 + 6*x + 9) )
Time = 2.28 (sec) , antiderivative size = 201, normalized size of antiderivative = 8.38 \[ \int \frac {e^{\frac {2 \left (189 x+198 x^2+111 x^3+30 x^4+3 x^5+e^8 \left (432 x+288 x^2+48 x^3\right )+e^4 \left (216 x+432 x^2+192 x^3+24 x^4\right )\right )}{9+6 x+x^2}} \left (1134+1998 x+1998 x^2+942 x^3+210 x^4+18 x^5+e^8 \left (2592+2592 x+864 x^2+96 x^3\right )+e^4 \left (1296+4752 x+3456 x^2+960 x^3+96 x^4\right )\right )}{27+27 x+9 x^2+x^3} \, dx={\mathrm {e}}^{\frac {6\,x^5}{x^2+6\,x+9}}\,{\mathrm {e}}^{\frac {60\,x^4}{x^2+6\,x+9}}\,{\mathrm {e}}^{\frac {222\,x^3}{x^2+6\,x+9}}\,{\mathrm {e}}^{\frac {396\,x^2}{x^2+6\,x+9}}\,{\mathrm {e}}^{\frac {432\,x\,{\mathrm {e}}^4}{x^2+6\,x+9}}\,{\mathrm {e}}^{\frac {864\,x\,{\mathrm {e}}^8}{x^2+6\,x+9}}\,{\mathrm {e}}^{\frac {48\,x^4\,{\mathrm {e}}^4}{x^2+6\,x+9}}\,{\mathrm {e}}^{\frac {96\,x^3\,{\mathrm {e}}^8}{x^2+6\,x+9}}\,{\mathrm {e}}^{\frac {384\,x^3\,{\mathrm {e}}^4}{x^2+6\,x+9}}\,{\mathrm {e}}^{\frac {576\,x^2\,{\mathrm {e}}^8}{x^2+6\,x+9}}\,{\mathrm {e}}^{\frac {864\,x^2\,{\mathrm {e}}^4}{x^2+6\,x+9}}\,{\mathrm {e}}^{\frac {378\,x}{x^2+6\,x+9}} \] Input:
int((exp((2*(189*x + exp(8)*(432*x + 288*x^2 + 48*x^3) + exp(4)*(216*x + 4 32*x^2 + 192*x^3 + 24*x^4) + 198*x^2 + 111*x^3 + 30*x^4 + 3*x^5))/(6*x + x ^2 + 9))*(1998*x + exp(8)*(2592*x + 864*x^2 + 96*x^3 + 2592) + exp(4)*(475 2*x + 3456*x^2 + 960*x^3 + 96*x^4 + 1296) + 1998*x^2 + 942*x^3 + 210*x^4 + 18*x^5 + 1134))/(27*x + 9*x^2 + x^3 + 27),x)
Output:
exp((6*x^5)/(6*x + x^2 + 9))*exp((60*x^4)/(6*x + x^2 + 9))*exp((222*x^3)/( 6*x + x^2 + 9))*exp((396*x^2)/(6*x + x^2 + 9))*exp((432*x*exp(4))/(6*x + x ^2 + 9))*exp((864*x*exp(8))/(6*x + x^2 + 9))*exp((48*x^4*exp(4))/(6*x + x^ 2 + 9))*exp((96*x^3*exp(8))/(6*x + x^2 + 9))*exp((384*x^3*exp(4))/(6*x + x ^2 + 9))*exp((576*x^2*exp(8))/(6*x + x^2 + 9))*exp((864*x^2*exp(4))/(6*x + x^2 + 9))*exp((378*x)/(6*x + x^2 + 9))
\[ \int \frac {e^{\frac {2 \left (189 x+198 x^2+111 x^3+30 x^4+3 x^5+e^8 \left (432 x+288 x^2+48 x^3\right )+e^4 \left (216 x+432 x^2+192 x^3+24 x^4\right )\right )}{9+6 x+x^2}} \left (1134+1998 x+1998 x^2+942 x^3+210 x^4+18 x^5+e^8 \left (2592+2592 x+864 x^2+96 x^3\right )+e^4 \left (1296+4752 x+3456 x^2+960 x^3+96 x^4\right )\right )}{27+27 x+9 x^2+x^3} \, dx=\int \frac {\left (\left (96 x^{3}+864 x^{2}+2592 x +2592\right ) \left ({\mathrm e}^{4}\right )^{2}+\left (96 x^{4}+960 x^{3}+3456 x^{2}+4752 x +1296\right ) {\mathrm e}^{4}+18 x^{5}+210 x^{4}+942 x^{3}+1998 x^{2}+1998 x +1134\right ) \left ({\mathrm e}^{\frac {\left (48 x^{3}+288 x^{2}+432 x \right ) \left ({\mathrm e}^{4}\right )^{2}+\left (24 x^{4}+192 x^{3}+432 x^{2}+216 x \right ) {\mathrm e}^{4}+3 x^{5}+30 x^{4}+111 x^{3}+198 x^{2}+189 x}{x^{2}+6 x +9}}\right )^{2}}{x^{3}+9 x^{2}+27 x +27}d x \] Input:
int(((96*x^3+864*x^2+2592*x+2592)*exp(4)^2+(96*x^4+960*x^3+3456*x^2+4752*x +1296)*exp(4)+18*x^5+210*x^4+942*x^3+1998*x^2+1998*x+1134)*exp(((48*x^3+28 8*x^2+432*x)*exp(4)^2+(24*x^4+192*x^3+432*x^2+216*x)*exp(4)+3*x^5+30*x^4+1 11*x^3+198*x^2+189*x)/(x^2+6*x+9))^2/(x^3+9*x^2+27*x+27),x)
Output:
int(((96*x^3+864*x^2+2592*x+2592)*exp(4)^2+(96*x^4+960*x^3+3456*x^2+4752*x +1296)*exp(4)+18*x^5+210*x^4+942*x^3+1998*x^2+1998*x+1134)*exp(((48*x^3+28 8*x^2+432*x)*exp(4)^2+(24*x^4+192*x^3+432*x^2+216*x)*exp(4)+3*x^5+30*x^4+1 11*x^3+198*x^2+189*x)/(x^2+6*x+9))^2/(x^3+9*x^2+27*x+27),x)