Integrand size = 294, antiderivative size = 31 \[ \int \frac {18+6 x-22 x^2-6 x^3+6 x^4+2 x^5+e^8 (2+2 x)+e^4 \left (12+8 x-8 x^2-4 x^3\right )+e^{2 e^x} \left (2 x^2+2 x^3\right )+e^{e^x} \left (12 x+8 x^2-8 x^3-4 x^4+e^4 \left (4 x+4 x^2\right )\right )+e^{\frac {1}{3+e^4-x+e^{e^x} x-x^2}} \left (-9-e^8+5 x+3 x^2-e^{2 e^x} x^2-2 x^3-x^4+e^4 \left (-6+2 x+2 x^2\right )+e^{e^x} \left (-5 x-2 e^4 x+2 x^2+e^x x^2+2 x^3\right )\right )}{9+e^8-6 x-5 x^2+e^{2 e^x} x^2+2 x^3+x^4+e^4 \left (6-2 x-2 x^2\right )+e^{e^x} \left (6 x+2 e^4 x-2 x^2-2 x^3\right )} \, dx=x \left (2-e^{\frac {1}{3+e^4-x+e^{e^x} x-x^2}}+x\right ) \] Output:
(2-exp(1/(x*exp(exp(x))+exp(4)-x^2-x+3))+x)*x
Time = 0.20 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.00 \[ \int \frac {18+6 x-22 x^2-6 x^3+6 x^4+2 x^5+e^8 (2+2 x)+e^4 \left (12+8 x-8 x^2-4 x^3\right )+e^{2 e^x} \left (2 x^2+2 x^3\right )+e^{e^x} \left (12 x+8 x^2-8 x^3-4 x^4+e^4 \left (4 x+4 x^2\right )\right )+e^{\frac {1}{3+e^4-x+e^{e^x} x-x^2}} \left (-9-e^8+5 x+3 x^2-e^{2 e^x} x^2-2 x^3-x^4+e^4 \left (-6+2 x+2 x^2\right )+e^{e^x} \left (-5 x-2 e^4 x+2 x^2+e^x x^2+2 x^3\right )\right )}{9+e^8-6 x-5 x^2+e^{2 e^x} x^2+2 x^3+x^4+e^4 \left (6-2 x-2 x^2\right )+e^{e^x} \left (6 x+2 e^4 x-2 x^2-2 x^3\right )} \, dx=x \left (2-e^{\frac {1}{3+e^4-x+e^{e^x} x-x^2}}+x\right ) \] Input:
Integrate[(18 + 6*x - 22*x^2 - 6*x^3 + 6*x^4 + 2*x^5 + E^8*(2 + 2*x) + E^4 *(12 + 8*x - 8*x^2 - 4*x^3) + E^(2*E^x)*(2*x^2 + 2*x^3) + E^E^x*(12*x + 8* x^2 - 8*x^3 - 4*x^4 + E^4*(4*x + 4*x^2)) + E^(3 + E^4 - x + E^E^x*x - x^2) ^(-1)*(-9 - E^8 + 5*x + 3*x^2 - E^(2*E^x)*x^2 - 2*x^3 - x^4 + E^4*(-6 + 2* x + 2*x^2) + E^E^x*(-5*x - 2*E^4*x + 2*x^2 + E^x*x^2 + 2*x^3)))/(9 + E^8 - 6*x - 5*x^2 + E^(2*E^x)*x^2 + 2*x^3 + x^4 + E^4*(6 - 2*x - 2*x^2) + E^E^x *(6*x + 2*E^4*x - 2*x^2 - 2*x^3)),x]
Output:
x*(2 - E^(3 + E^4 - x + E^E^x*x - x^2)^(-1) + x)
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.
| \(\displaystyle \int \frac {2 x^5+6 x^4-6 x^3-22 x^2+e^4 \left (-4 x^3-8 x^2+8 x+12\right )+e^{2 e^x} \left (2 x^3+2 x^2\right )+e^{e^x} \left (-4 x^4-8 x^3+8 x^2+e^4 \left (4 x^2+4 x\right )+12 x\right )+e^{\frac {1}{-x^2+e^{e^x} x-x+e^4+3}} \left (-x^4-2 x^3-e^{2 e^x} x^2+3 x^2+e^4 \left (2 x^2+2 x-6\right )+e^{e^x} \left (2 x^3+e^x x^2+2 x^2-2 e^4 x-5 x\right )+5 x-e^8-9\right )+6 x+e^8 (2 x+2)+18}{x^4+2 x^3+e^{2 e^x} x^2-5 x^2+e^4 \left (-2 x^2-2 x+6\right )+e^{e^x} \left (-2 x^3-2 x^2+2 e^4 x+6 x\right )-6 x+e^8+9} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {2 x^5+6 x^4-6 x^3-22 x^2+e^4 \left (-4 x^3-8 x^2+8 x+12\right )+e^{2 e^x} \left (2 x^3+2 x^2\right )+e^{e^x} \left (-4 x^4-8 x^3+8 x^2+e^4 \left (4 x^2+4 x\right )+12 x\right )+e^{\frac {1}{-x^2+e^{e^x} x-x+e^4+3}} \left (-x^4-2 x^3-e^{2 e^x} x^2+3 x^2+e^4 \left (2 x^2+2 x-6\right )+e^{e^x} \left (2 x^3+e^x x^2+2 x^2-2 e^4 x-5 x\right )+5 x-e^8-9\right )+6 x+e^8 (2 x+2)+18}{\left (-x^2+e^{e^x} x-x+3 \left (1+\frac {e^4}{3}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 e^{2 e^x} (x+1) x^2}{\left (-x^2+e^{e^x} x-x+3 \left (1+\frac {e^4}{3}\right )\right )^2}-\frac {22 x^2}{\left (-x^2+e^{e^x} x-x+3 \left (1+\frac {e^4}{3}\right )\right )^2}+\frac {4 e^{e^x} (x+1) \left (-x^2-x+e^4+3\right ) x}{\left (-x^2+e^{e^x} x-x+3 \left (1+\frac {e^4}{3}\right )\right )^2}+\frac {6 x}{\left (-x^2+e^{e^x} x-x+3 \left (1+\frac {e^4}{3}\right )\right )^2}+\frac {2 e^8 (x+1)}{\left (-x^2+e^{e^x} x-x+3 \left (1+\frac {e^4}{3}\right )\right )^2}+\frac {4 e^4 (x+1) \left (-x^2-x+3\right )}{\left (-x^2+e^{e^x} x-x+3 \left (1+\frac {e^4}{3}\right )\right )^2}+\frac {18}{\left (-x^2+e^{e^x} x-x+3 \left (1+\frac {e^4}{3}\right )\right )^2}+\frac {2 x^5}{\left (-x^2+e^{e^x} x-x+3 \left (1+\frac {e^4}{3}\right )\right )^2}+\frac {6 x^4}{\left (-x^2+e^{e^x} x-x+3 \left (1+\frac {e^4}{3}\right )\right )^2}-\frac {6 x^3}{\left (-x^2+e^{e^x} x-x+3 \left (1+\frac {e^4}{3}\right )\right )^2}+\frac {e^{\frac {1}{-x^2+e^{e^x} x-x+3 \left (1+\frac {e^4}{3}\right )}} \left (-x^4+2 e^{e^x} x^3-2 x^3+2 e^{e^x} x^2-e^{2 e^x} x^2+e^{x+e^x} x^2+3 \left (1+\frac {2 e^4}{3}\right ) x^2-5 \left (1+\frac {2 e^4}{5}\right ) e^{e^x} x+5 \left (1+\frac {2 e^4}{5}\right ) x-9 \left (1+\frac {1}{9} e^4 \left (6+e^4\right )\right )\right )}{\left (-x^2+e^{e^x} x-x+3 \left (1+\frac {e^4}{3}\right )\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle \int \left (\frac {2 e^{2 e^x} (x+1) x^2}{\left (-x^2+e^{e^x} x-x+3 \left (1+\frac {e^4}{3}\right )\right )^2}-\frac {22 x^2}{\left (-x^2+e^{e^x} x-x+3 \left (1+\frac {e^4}{3}\right )\right )^2}+\frac {4 e^{e^x} (x+1) \left (-x^2-x+e^4+3\right ) x}{\left (-x^2+e^{e^x} x-x+3 \left (1+\frac {e^4}{3}\right )\right )^2}+\frac {6 x}{\left (-x^2+e^{e^x} x-x+3 \left (1+\frac {e^4}{3}\right )\right )^2}+\frac {2 e^8 (x+1)}{\left (-x^2+e^{e^x} x-x+3 \left (1+\frac {e^4}{3}\right )\right )^2}+\frac {4 e^4 (x+1) \left (-x^2-x+3\right )}{\left (-x^2+e^{e^x} x-x+3 \left (1+\frac {e^4}{3}\right )\right )^2}+\frac {18}{\left (-x^2+e^{e^x} x-x+3 \left (1+\frac {e^4}{3}\right )\right )^2}+\frac {2 x^5}{\left (-x^2+e^{e^x} x-x+3 \left (1+\frac {e^4}{3}\right )\right )^2}+\frac {6 x^4}{\left (-x^2+e^{e^x} x-x+3 \left (1+\frac {e^4}{3}\right )\right )^2}-\frac {6 x^3}{\left (-x^2+e^{e^x} x-x+3 \left (1+\frac {e^4}{3}\right )\right )^2}+\frac {e^{\frac {1}{-x^2+e^{e^x} x-x+3 \left (1+\frac {e^4}{3}\right )}} \left (-x^4+2 e^{e^x} x^3-2 x^3+2 e^{e^x} x^2-e^{2 e^x} x^2+e^{x+e^x} x^2+3 \left (1+\frac {2 e^4}{3}\right ) x^2-5 \left (1+\frac {2 e^4}{5}\right ) e^{e^x} x+5 \left (1+\frac {2 e^4}{5}\right ) x-9 \left (1+\frac {1}{9} e^4 \left (6+e^4\right )\right )\right )}{\left (-x^2+e^{e^x} x-x+3 \left (1+\frac {e^4}{3}\right )\right )^2}\right )dx\) |
Input:
Int[(18 + 6*x - 22*x^2 - 6*x^3 + 6*x^4 + 2*x^5 + E^8*(2 + 2*x) + E^4*(12 + 8*x - 8*x^2 - 4*x^3) + E^(2*E^x)*(2*x^2 + 2*x^3) + E^E^x*(12*x + 8*x^2 - 8*x^3 - 4*x^4 + E^4*(4*x + 4*x^2)) + E^(3 + E^4 - x + E^E^x*x - x^2)^(-1)* (-9 - E^8 + 5*x + 3*x^2 - E^(2*E^x)*x^2 - 2*x^3 - x^4 + E^4*(-6 + 2*x + 2* x^2) + E^E^x*(-5*x - 2*E^4*x + 2*x^2 + E^x*x^2 + 2*x^3)))/(9 + E^8 - 6*x - 5*x^2 + E^(2*E^x)*x^2 + 2*x^3 + x^4 + E^4*(6 - 2*x - 2*x^2) + E^E^x*(6*x + 2*E^4*x - 2*x^2 - 2*x^3)),x]
Output:
$Aborted
Time = 48.58 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.00
| method | result | size |
| risch | \(x^{2}-{\mathrm e}^{\frac {1}{x \,{\mathrm e}^{{\mathrm e}^{x}}+{\mathrm e}^{4}-x^{2}-x +3}} x +2 x\) | \(31\) |
| parallelrisch | \(x^{2}-{\mathrm e}^{\frac {1}{x \,{\mathrm e}^{{\mathrm e}^{x}}+{\mathrm e}^{4}-x^{2}-x +3}} x +2 x\) | \(31\) |
Input:
int(((-x^2*exp(exp(x))^2+(exp(x)*x^2-2*x*exp(4)+2*x^3+2*x^2-5*x)*exp(exp(x ))-exp(4)^2+(2*x^2+2*x-6)*exp(4)-x^4-2*x^3+3*x^2+5*x-9)*exp(1/(x*exp(exp(x ))+exp(4)-x^2-x+3))+(2*x^3+2*x^2)*exp(exp(x))^2+((4*x^2+4*x)*exp(4)-4*x^4- 8*x^3+8*x^2+12*x)*exp(exp(x))+(2+2*x)*exp(4)^2+(-4*x^3-8*x^2+8*x+12)*exp(4 )+2*x^5+6*x^4-6*x^3-22*x^2+6*x+18)/(x^2*exp(exp(x))^2+(2*x*exp(4)-2*x^3-2* x^2+6*x)*exp(exp(x))+exp(4)^2+(-2*x^2-2*x+6)*exp(4)+x^4+2*x^3-5*x^2-6*x+9) ,x,method=_RETURNVERBOSE)
Output:
x^2-exp(1/(x*exp(exp(x))+exp(4)-x^2-x+3))*x+2*x
Time = 0.10 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.00 \[ \int \frac {18+6 x-22 x^2-6 x^3+6 x^4+2 x^5+e^8 (2+2 x)+e^4 \left (12+8 x-8 x^2-4 x^3\right )+e^{2 e^x} \left (2 x^2+2 x^3\right )+e^{e^x} \left (12 x+8 x^2-8 x^3-4 x^4+e^4 \left (4 x+4 x^2\right )\right )+e^{\frac {1}{3+e^4-x+e^{e^x} x-x^2}} \left (-9-e^8+5 x+3 x^2-e^{2 e^x} x^2-2 x^3-x^4+e^4 \left (-6+2 x+2 x^2\right )+e^{e^x} \left (-5 x-2 e^4 x+2 x^2+e^x x^2+2 x^3\right )\right )}{9+e^8-6 x-5 x^2+e^{2 e^x} x^2+2 x^3+x^4+e^4 \left (6-2 x-2 x^2\right )+e^{e^x} \left (6 x+2 e^4 x-2 x^2-2 x^3\right )} \, dx=x^{2} - x e^{\left (-\frac {1}{x^{2} - x e^{\left (e^{x}\right )} + x - e^{4} - 3}\right )} + 2 \, x \] Input:
integrate(((-x^2*exp(exp(x))^2+(exp(x)*x^2-2*x*exp(4)+2*x^3+2*x^2-5*x)*exp (exp(x))-exp(4)^2+(2*x^2+2*x-6)*exp(4)-x^4-2*x^3+3*x^2+5*x-9)*exp(1/(x*exp (exp(x))+exp(4)-x^2-x+3))+(2*x^3+2*x^2)*exp(exp(x))^2+((4*x^2+4*x)*exp(4)- 4*x^4-8*x^3+8*x^2+12*x)*exp(exp(x))+(2+2*x)*exp(4)^2+(-4*x^3-8*x^2+8*x+12) *exp(4)+2*x^5+6*x^4-6*x^3-22*x^2+6*x+18)/(x^2*exp(exp(x))^2+(2*x*exp(4)-2* x^3-2*x^2+6*x)*exp(exp(x))+exp(4)^2+(-2*x^2-2*x+6)*exp(4)+x^4+2*x^3-5*x^2- 6*x+9),x, algorithm="fricas")
Output:
x^2 - x*e^(-1/(x^2 - x*e^(e^x) + x - e^4 - 3)) + 2*x
Time = 8.38 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.87 \[ \int \frac {18+6 x-22 x^2-6 x^3+6 x^4+2 x^5+e^8 (2+2 x)+e^4 \left (12+8 x-8 x^2-4 x^3\right )+e^{2 e^x} \left (2 x^2+2 x^3\right )+e^{e^x} \left (12 x+8 x^2-8 x^3-4 x^4+e^4 \left (4 x+4 x^2\right )\right )+e^{\frac {1}{3+e^4-x+e^{e^x} x-x^2}} \left (-9-e^8+5 x+3 x^2-e^{2 e^x} x^2-2 x^3-x^4+e^4 \left (-6+2 x+2 x^2\right )+e^{e^x} \left (-5 x-2 e^4 x+2 x^2+e^x x^2+2 x^3\right )\right )}{9+e^8-6 x-5 x^2+e^{2 e^x} x^2+2 x^3+x^4+e^4 \left (6-2 x-2 x^2\right )+e^{e^x} \left (6 x+2 e^4 x-2 x^2-2 x^3\right )} \, dx=x^{2} - x e^{\frac {1}{- x^{2} + x e^{e^{x}} - x + 3 + e^{4}}} + 2 x \] Input:
integrate(((-x**2*exp(exp(x))**2+(exp(x)*x**2-2*x*exp(4)+2*x**3+2*x**2-5*x )*exp(exp(x))-exp(4)**2+(2*x**2+2*x-6)*exp(4)-x**4-2*x**3+3*x**2+5*x-9)*ex p(1/(x*exp(exp(x))+exp(4)-x**2-x+3))+(2*x**3+2*x**2)*exp(exp(x))**2+((4*x* *2+4*x)*exp(4)-4*x**4-8*x**3+8*x**2+12*x)*exp(exp(x))+(2+2*x)*exp(4)**2+(- 4*x**3-8*x**2+8*x+12)*exp(4)+2*x**5+6*x**4-6*x**3-22*x**2+6*x+18)/(x**2*ex p(exp(x))**2+(2*x*exp(4)-2*x**3-2*x**2+6*x)*exp(exp(x))+exp(4)**2+(-2*x**2 -2*x+6)*exp(4)+x**4+2*x**3-5*x**2-6*x+9),x)
Output:
x**2 - x*exp(1/(-x**2 + x*exp(exp(x)) - x + 3 + exp(4))) + 2*x
\[ \int \frac {18+6 x-22 x^2-6 x^3+6 x^4+2 x^5+e^8 (2+2 x)+e^4 \left (12+8 x-8 x^2-4 x^3\right )+e^{2 e^x} \left (2 x^2+2 x^3\right )+e^{e^x} \left (12 x+8 x^2-8 x^3-4 x^4+e^4 \left (4 x+4 x^2\right )\right )+e^{\frac {1}{3+e^4-x+e^{e^x} x-x^2}} \left (-9-e^8+5 x+3 x^2-e^{2 e^x} x^2-2 x^3-x^4+e^4 \left (-6+2 x+2 x^2\right )+e^{e^x} \left (-5 x-2 e^4 x+2 x^2+e^x x^2+2 x^3\right )\right )}{9+e^8-6 x-5 x^2+e^{2 e^x} x^2+2 x^3+x^4+e^4 \left (6-2 x-2 x^2\right )+e^{e^x} \left (6 x+2 e^4 x-2 x^2-2 x^3\right )} \, dx=\int { \frac {2 \, x^{5} + 6 \, x^{4} - 6 \, x^{3} - 22 \, x^{2} + 2 \, {\left (x + 1\right )} e^{8} - 4 \, {\left (x^{3} + 2 \, x^{2} - 2 \, x - 3\right )} e^{4} + 2 \, {\left (x^{3} + x^{2}\right )} e^{\left (2 \, e^{x}\right )} - {\left (x^{4} + 2 \, x^{3} + x^{2} e^{\left (2 \, e^{x}\right )} - 3 \, x^{2} - 2 \, {\left (x^{2} + x - 3\right )} e^{4} - {\left (2 \, x^{3} + x^{2} e^{x} + 2 \, x^{2} - 2 \, x e^{4} - 5 \, x\right )} e^{\left (e^{x}\right )} - 5 \, x + e^{8} + 9\right )} e^{\left (-\frac {1}{x^{2} - x e^{\left (e^{x}\right )} + x - e^{4} - 3}\right )} - 4 \, {\left (x^{4} + 2 \, x^{3} - 2 \, x^{2} - {\left (x^{2} + x\right )} e^{4} - 3 \, x\right )} e^{\left (e^{x}\right )} + 6 \, x + 18}{x^{4} + 2 \, x^{3} + x^{2} e^{\left (2 \, e^{x}\right )} - 5 \, x^{2} - 2 \, {\left (x^{2} + x - 3\right )} e^{4} - 2 \, {\left (x^{3} + x^{2} - x e^{4} - 3 \, x\right )} e^{\left (e^{x}\right )} - 6 \, x + e^{8} + 9} \,d x } \] Input:
integrate(((-x^2*exp(exp(x))^2+(exp(x)*x^2-2*x*exp(4)+2*x^3+2*x^2-5*x)*exp (exp(x))-exp(4)^2+(2*x^2+2*x-6)*exp(4)-x^4-2*x^3+3*x^2+5*x-9)*exp(1/(x*exp (exp(x))+exp(4)-x^2-x+3))+(2*x^3+2*x^2)*exp(exp(x))^2+((4*x^2+4*x)*exp(4)- 4*x^4-8*x^3+8*x^2+12*x)*exp(exp(x))+(2+2*x)*exp(4)^2+(-4*x^3-8*x^2+8*x+12) *exp(4)+2*x^5+6*x^4-6*x^3-22*x^2+6*x+18)/(x^2*exp(exp(x))^2+(2*x*exp(4)-2* x^3-2*x^2+6*x)*exp(exp(x))+exp(4)^2+(-2*x^2-2*x+6)*exp(4)+x^4+2*x^3-5*x^2- 6*x+9),x, algorithm="maxima")
Output:
x^2 + 2*x - integrate((x^4 + 2*x^3 - x^2*(2*e^4 + 3) + x^2*e^(2*e^x) - x*( 2*e^4 + 5) - (2*x^3 + x^2*e^x + 2*x^2 - x*(2*e^4 + 5))*e^(e^x) + e^8 + 6*e ^4 + 9)*e^(-1/(x^2 - x*e^(e^x) + x - e^4 - 3))/(x^4 + 2*x^3 - x^2*(2*e^4 + 5) + x^2*e^(2*e^x) - 2*x*(e^4 + 3) - 2*(x^3 + x^2 - x*(e^4 + 3))*e^(e^x) + e^8 + 6*e^4 + 9), x)
Timed out. \[ \int \frac {18+6 x-22 x^2-6 x^3+6 x^4+2 x^5+e^8 (2+2 x)+e^4 \left (12+8 x-8 x^2-4 x^3\right )+e^{2 e^x} \left (2 x^2+2 x^3\right )+e^{e^x} \left (12 x+8 x^2-8 x^3-4 x^4+e^4 \left (4 x+4 x^2\right )\right )+e^{\frac {1}{3+e^4-x+e^{e^x} x-x^2}} \left (-9-e^8+5 x+3 x^2-e^{2 e^x} x^2-2 x^3-x^4+e^4 \left (-6+2 x+2 x^2\right )+e^{e^x} \left (-5 x-2 e^4 x+2 x^2+e^x x^2+2 x^3\right )\right )}{9+e^8-6 x-5 x^2+e^{2 e^x} x^2+2 x^3+x^4+e^4 \left (6-2 x-2 x^2\right )+e^{e^x} \left (6 x+2 e^4 x-2 x^2-2 x^3\right )} \, dx=\text {Timed out} \] Input:
integrate(((-x^2*exp(exp(x))^2+(exp(x)*x^2-2*x*exp(4)+2*x^3+2*x^2-5*x)*exp (exp(x))-exp(4)^2+(2*x^2+2*x-6)*exp(4)-x^4-2*x^3+3*x^2+5*x-9)*exp(1/(x*exp (exp(x))+exp(4)-x^2-x+3))+(2*x^3+2*x^2)*exp(exp(x))^2+((4*x^2+4*x)*exp(4)- 4*x^4-8*x^3+8*x^2+12*x)*exp(exp(x))+(2+2*x)*exp(4)^2+(-4*x^3-8*x^2+8*x+12) *exp(4)+2*x^5+6*x^4-6*x^3-22*x^2+6*x+18)/(x^2*exp(exp(x))^2+(2*x*exp(4)-2* x^3-2*x^2+6*x)*exp(exp(x))+exp(4)^2+(-2*x^2-2*x+6)*exp(4)+x^4+2*x^3-5*x^2- 6*x+9),x, algorithm="giac")
Output:
Timed out
Time = 4.29 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.87 \[ \int \frac {18+6 x-22 x^2-6 x^3+6 x^4+2 x^5+e^8 (2+2 x)+e^4 \left (12+8 x-8 x^2-4 x^3\right )+e^{2 e^x} \left (2 x^2+2 x^3\right )+e^{e^x} \left (12 x+8 x^2-8 x^3-4 x^4+e^4 \left (4 x+4 x^2\right )\right )+e^{\frac {1}{3+e^4-x+e^{e^x} x-x^2}} \left (-9-e^8+5 x+3 x^2-e^{2 e^x} x^2-2 x^3-x^4+e^4 \left (-6+2 x+2 x^2\right )+e^{e^x} \left (-5 x-2 e^4 x+2 x^2+e^x x^2+2 x^3\right )\right )}{9+e^8-6 x-5 x^2+e^{2 e^x} x^2+2 x^3+x^4+e^4 \left (6-2 x-2 x^2\right )+e^{e^x} \left (6 x+2 e^4 x-2 x^2-2 x^3\right )} \, dx=x\,\left (x-{\mathrm {e}}^{\frac {1}{{\mathrm {e}}^4-x+x\,{\mathrm {e}}^{{\mathrm {e}}^x}-x^2+3}}+2\right ) \] Input:
int((6*x + exp(4)*(8*x - 8*x^2 - 4*x^3 + 12) - exp(1/(exp(4) - x + x*exp(e xp(x)) - x^2 + 3))*(exp(8) - 5*x - exp(4)*(2*x + 2*x^2 - 6) - exp(exp(x))* (x^2*exp(x) - 5*x - 2*x*exp(4) + 2*x^2 + 2*x^3) - 3*x^2 + 2*x^3 + x^4 + x^ 2*exp(2*exp(x)) + 9) + exp(exp(x))*(12*x + exp(4)*(4*x + 4*x^2) + 8*x^2 - 8*x^3 - 4*x^4) + exp(2*exp(x))*(2*x^2 + 2*x^3) - 22*x^2 - 6*x^3 + 6*x^4 + 2*x^5 + exp(8)*(2*x + 2) + 18)/(exp(8) - 6*x - exp(4)*(2*x + 2*x^2 - 6) + exp(exp(x))*(6*x + 2*x*exp(4) - 2*x^2 - 2*x^3) - 5*x^2 + 2*x^3 + x^4 + x^2 *exp(2*exp(x)) + 9),x)
Output:
x*(x - exp(1/(exp(4) - x + x*exp(exp(x)) - x^2 + 3)) + 2)
Time = 0.22 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.00 \[ \int \frac {18+6 x-22 x^2-6 x^3+6 x^4+2 x^5+e^8 (2+2 x)+e^4 \left (12+8 x-8 x^2-4 x^3\right )+e^{2 e^x} \left (2 x^2+2 x^3\right )+e^{e^x} \left (12 x+8 x^2-8 x^3-4 x^4+e^4 \left (4 x+4 x^2\right )\right )+e^{\frac {1}{3+e^4-x+e^{e^x} x-x^2}} \left (-9-e^8+5 x+3 x^2-e^{2 e^x} x^2-2 x^3-x^4+e^4 \left (-6+2 x+2 x^2\right )+e^{e^x} \left (-5 x-2 e^4 x+2 x^2+e^x x^2+2 x^3\right )\right )}{9+e^8-6 x-5 x^2+e^{2 e^x} x^2+2 x^3+x^4+e^4 \left (6-2 x-2 x^2\right )+e^{e^x} \left (6 x+2 e^4 x-2 x^2-2 x^3\right )} \, dx=x \left (-e^{\frac {1}{e^{e^{x}} x +e^{4}-x^{2}-x +3}}+x +2\right ) \] Input:
int(((-x^2*exp(exp(x))^2+(exp(x)*x^2-2*x*exp(4)+2*x^3+2*x^2-5*x)*exp(exp(x ))-exp(4)^2+(2*x^2+2*x-6)*exp(4)-x^4-2*x^3+3*x^2+5*x-9)*exp(1/(x*exp(exp(x ))+exp(4)-x^2-x+3))+(2*x^3+2*x^2)*exp(exp(x))^2+((4*x^2+4*x)*exp(4)-4*x^4- 8*x^3+8*x^2+12*x)*exp(exp(x))+(2+2*x)*exp(4)^2+(-4*x^3-8*x^2+8*x+12)*exp(4 )+2*x^5+6*x^4-6*x^3-22*x^2+6*x+18)/(x^2*exp(exp(x))^2+(2*x*exp(4)-2*x^3-2* x^2+6*x)*exp(exp(x))+exp(4)^2+(-2*x^2-2*x+6)*exp(4)+x^4+2*x^3-5*x^2-6*x+9) ,x)
Output:
x*( - e**(1/(e**(e**x)*x + e**4 - x**2 - x + 3)) + x + 2)