Integrand size = 181, antiderivative size = 30 \[ \int \frac {-64 e^6+224 e^4 x-243 e^2 x^2+81 x^3+e^{2 e^x} \left (-4 e^6+12 e^4 x-12 e^2 x^2+4 x^3+e^x \left (-8 e^6 x+24 e^4 x^2-24 e^2 x^3+8 x^4\right )\right )+e^{e^x} \left (-32 e^6+104 e^4 x-108 e^2 x^2+36 x^3+e^x \left (-32 e^6 x+100 e^4 x^2-104 e^2 x^3+36 x^4\right )\right )}{4 e^6-12 e^4 x+12 e^2 x^2-4 x^3} \, dx=\frac {70}{9}-x \left (4+e^{e^x}+\frac {x}{2 \left (-e^2+x\right )}\right )^2 \] Output:
70/9-x*(exp(exp(x))+1/2*x/(x-exp(2))+4)^2
Leaf count is larger than twice the leaf count of optimal. \(72\) vs. \(2(30)=60\).
Time = 0.07 (sec) , antiderivative size = 72, normalized size of antiderivative = 2.40 \[ \int \frac {-64 e^6+224 e^4 x-243 e^2 x^2+81 x^3+e^{2 e^x} \left (-4 e^6+12 e^4 x-12 e^2 x^2+4 x^3+e^x \left (-8 e^6 x+24 e^4 x^2-24 e^2 x^3+8 x^4\right )\right )+e^{e^x} \left (-32 e^6+104 e^4 x-108 e^2 x^2+36 x^3+e^x \left (-32 e^6 x+100 e^4 x^2-104 e^2 x^3+36 x^4\right )\right )}{4 e^6-12 e^4 x+12 e^2 x^2-4 x^3} \, dx=\frac {1}{4} \left (-\frac {e^6}{\left (e^2-x\right )^2}-81 x-4 e^{2 e^x} x-\frac {4 e^{e^x} \left (8 e^2-9 x\right ) x}{e^2-x}-\frac {19 e^4}{-e^2+x}\right ) \] Input:
Integrate[(-64*E^6 + 224*E^4*x - 243*E^2*x^2 + 81*x^3 + E^(2*E^x)*(-4*E^6 + 12*E^4*x - 12*E^2*x^2 + 4*x^3 + E^x*(-8*E^6*x + 24*E^4*x^2 - 24*E^2*x^3 + 8*x^4)) + E^E^x*(-32*E^6 + 104*E^4*x - 108*E^2*x^2 + 36*x^3 + E^x*(-32*E ^6*x + 100*E^4*x^2 - 104*E^2*x^3 + 36*x^4)))/(4*E^6 - 12*E^4*x + 12*E^2*x^ 2 - 4*x^3),x]
Output:
(-(E^6/(E^2 - x)^2) - 81*x - 4*E^(2*E^x)*x - (4*E^E^x*(8*E^2 - 9*x)*x)/(E^ 2 - x) - (19*E^4)/(-E^2 + x))/4
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.
| \(\displaystyle \int \frac {81 x^3-243 e^2 x^2+e^{2 e^x} \left (4 x^3-12 e^2 x^2+e^x \left (8 x^4-24 e^2 x^3+24 e^4 x^2-8 e^6 x\right )+12 e^4 x-4 e^6\right )+e^{e^x} \left (36 x^3-108 e^2 x^2+e^x \left (36 x^4-104 e^2 x^3+100 e^4 x^2-32 e^6 x\right )+104 e^4 x-32 e^6\right )+224 e^4 x-64 e^6}{-4 x^3+12 e^2 x^2-12 e^4 x+4 e^6} \, dx\) |
| \(\Big \downarrow \) 2007 |
| \(\displaystyle \int \frac {81 x^3-243 e^2 x^2+e^{2 e^x} \left (4 x^3-12 e^2 x^2+e^x \left (8 x^4-24 e^2 x^3+24 e^4 x^2-8 e^6 x\right )+12 e^4 x-4 e^6\right )+e^{e^x} \left (36 x^3-108 e^2 x^2+e^x \left (36 x^4-104 e^2 x^3+100 e^4 x^2-32 e^6 x\right )+104 e^4 x-32 e^6\right )+224 e^4 x-64 e^6}{\left (2^{2/3} e^2-2^{2/3} x\right )^3}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {\left (-2 e^{e^x} x-9 x+2 e^{e^x+2}+8 e^2\right ) \left (-4 e^{x+e^x} x^3-2 e^{e^x} x^2+8 e^{x+e^x+2} x^2-9 x^2+4 e^{e^x+2} x-4 e^{x+e^x+4} x+19 e^2 x-2 e^{e^x+4}-8 e^4\right )}{\left (2^{2/3} e^2-2^{2/3} x\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {e^{e^x} \left (-2 e^{e^x} x-9 x+2 e^{e^x+2}+8 e^2\right ) x^2}{2 \left (e^2-x\right )^3}-\frac {9 \left (-2 e^{e^x} x-9 x+2 e^{e^x+2}+8 e^2\right ) x^2}{4 \left (e^2-x\right )^3}-\frac {e^{x+e^x} \left (-2 e^{e^x} x-9 x+2 e^{e^x+2}+8 e^2\right ) x}{e^2-x}+\frac {e^{e^x+2} \left (-2 e^{e^x} x-9 x+2 e^{e^x+2}+8 e^2\right ) x}{\left (e^2-x\right )^3}+\frac {19 e^2 \left (-2 e^{e^x} x-9 x+2 e^{e^x+2}+8 e^2\right ) x}{4 \left (e^2-x\right )^3}-\frac {e^{e^x+4} \left (-2 e^{e^x} x-9 x+2 e^{e^x+2}+8 e^2\right )}{2 \left (e^2-x\right )^3}-\frac {2 e^4 \left (-2 e^{e^x} x-9 x+2 e^{e^x+2}+8 e^2\right )}{\left (e^2-x\right )^3}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -4 e^4 \int \frac {e^{e^x}}{\left (e^2-x\right )^2}dx+\frac {19}{2} e^2 \int \frac {e^{2+e^x}}{\left (e^2-x\right )^2}dx-\frac {9}{2} \int \frac {e^{4+e^x}}{\left (e^2-x\right )^2}dx+2 \int \frac {e^{2 \left (1+e^x\right )}}{e^2-x}dx+\frac {19}{2} \int \frac {e^{2+e^x}}{e^2-x}dx+\int \frac {e^{x+e^x+4}}{e^2-x}dx-9 \int e^{x+e^x} xdx-2 \int e^{x+2 e^x} xdx+\frac {19}{2} e^2 \int \frac {e^{e^x}}{x-e^2}dx+2 \int \frac {e^{2 \left (1+e^x\right )}}{x-e^2}dx-9 \operatorname {ExpIntegralEi}\left (e^x\right )-\operatorname {ExpIntegralEi}\left (2 e^x\right )+\frac {e^2 \left (8 e^2-9 x\right )^2}{\left (e^2-x\right )^2}-e^{e^x+2}-\frac {81 x}{4}+\frac {91 e^4}{4 \left (e^2-x\right )}-\frac {5 e^6}{4 \left (e^2-x\right )^2}\) |
Input:
Int[(-64*E^6 + 224*E^4*x - 243*E^2*x^2 + 81*x^3 + E^(2*E^x)*(-4*E^6 + 12*E ^4*x - 12*E^2*x^2 + 4*x^3 + E^x*(-8*E^6*x + 24*E^4*x^2 - 24*E^2*x^3 + 8*x^ 4)) + E^E^x*(-32*E^6 + 104*E^4*x - 108*E^2*x^2 + 36*x^3 + E^x*(-32*E^6*x + 100*E^4*x^2 - 104*E^2*x^3 + 36*x^4)))/(4*E^6 - 12*E^4*x + 12*E^2*x^2 - 4* x^3),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(58\) vs. \(2(23)=46\).
Time = 1.47 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.97
| method | result | size |
| risch | \(-\frac {81 x}{4}+\frac {\frac {9 \,{\mathrm e}^{6}}{2}-\frac {19 x \,{\mathrm e}^{4}}{4}}{{\mathrm e}^{4}-2 \,{\mathrm e}^{2} x +x^{2}}-x \,{\mathrm e}^{2 \,{\mathrm e}^{x}}-\frac {\left (8 \,{\mathrm e}^{2}-9 x \right ) x \,{\mathrm e}^{{\mathrm e}^{x}}}{{\mathrm e}^{2}-x}\) | \(59\) |
| norman | \(\frac {56 x \,{\mathrm e}^{4}-\frac {81 x^{3}}{4}-9 x^{3} {\mathrm e}^{{\mathrm e}^{x}}-{\mathrm e}^{2 \,{\mathrm e}^{x}} x^{3}+17 \,{\mathrm e}^{2} {\mathrm e}^{{\mathrm e}^{x}} x^{2}+2 \,{\mathrm e}^{2} {\mathrm e}^{2 \,{\mathrm e}^{x}} x^{2}-8 \,{\mathrm e}^{4} {\mathrm e}^{{\mathrm e}^{x}} x -{\mathrm e}^{4} {\mathrm e}^{2 \,{\mathrm e}^{x}} x -36 \,{\mathrm e}^{6}}{\left ({\mathrm e}^{2}-x \right )^{2}}\) | \(91\) |
| parallelrisch | \(-\frac {4 \,{\mathrm e}^{4} {\mathrm e}^{2 \,{\mathrm e}^{x}} x -8 \,{\mathrm e}^{2} {\mathrm e}^{2 \,{\mathrm e}^{x}} x^{2}+4 \,{\mathrm e}^{2 \,{\mathrm e}^{x}} x^{3}+32 \,{\mathrm e}^{4} {\mathrm e}^{{\mathrm e}^{x}} x -68 \,{\mathrm e}^{2} {\mathrm e}^{{\mathrm e}^{x}} x^{2}+36 x^{3} {\mathrm e}^{{\mathrm e}^{x}}+144 \,{\mathrm e}^{6}-224 x \,{\mathrm e}^{4}+81 x^{3}}{4 \left ({\mathrm e}^{4}-2 \,{\mathrm e}^{2} x +x^{2}\right )}\) | \(99\) |
Input:
int((((-8*x*exp(2)^3+24*x^2*exp(2)^2-24*x^3*exp(2)+8*x^4)*exp(x)-4*exp(2)^ 3+12*x*exp(2)^2-12*x^2*exp(2)+4*x^3)*exp(exp(x))^2+((-32*x*exp(2)^3+100*x^ 2*exp(2)^2-104*x^3*exp(2)+36*x^4)*exp(x)-32*exp(2)^3+104*x*exp(2)^2-108*x^ 2*exp(2)+36*x^3)*exp(exp(x))-64*exp(2)^3+224*x*exp(2)^2-243*x^2*exp(2)+81* x^3)/(4*exp(2)^3-12*x*exp(2)^2+12*x^2*exp(2)-4*x^3),x,method=_RETURNVERBOS E)
Output:
-81/4*x+(9/2*exp(6)-19/4*x*exp(4))/(exp(4)-2*exp(2)*x+x^2)-x*exp(2*exp(x)) -(8*exp(2)-9*x)*x/(exp(2)-x)*exp(exp(x))
Leaf count of result is larger than twice the leaf count of optimal. 82 vs. \(2 (24) = 48\).
Time = 0.11 (sec) , antiderivative size = 82, normalized size of antiderivative = 2.73 \[ \int \frac {-64 e^6+224 e^4 x-243 e^2 x^2+81 x^3+e^{2 e^x} \left (-4 e^6+12 e^4 x-12 e^2 x^2+4 x^3+e^x \left (-8 e^6 x+24 e^4 x^2-24 e^2 x^3+8 x^4\right )\right )+e^{e^x} \left (-32 e^6+104 e^4 x-108 e^2 x^2+36 x^3+e^x \left (-32 e^6 x+100 e^4 x^2-104 e^2 x^3+36 x^4\right )\right )}{4 e^6-12 e^4 x+12 e^2 x^2-4 x^3} \, dx=-\frac {81 \, x^{3} - 162 \, x^{2} e^{2} + 100 \, x e^{4} + 4 \, {\left (x^{3} - 2 \, x^{2} e^{2} + x e^{4}\right )} e^{\left (2 \, e^{x}\right )} + 4 \, {\left (9 \, x^{3} - 17 \, x^{2} e^{2} + 8 \, x e^{4}\right )} e^{\left (e^{x}\right )} - 18 \, e^{6}}{4 \, {\left (x^{2} - 2 \, x e^{2} + e^{4}\right )}} \] Input:
integrate((((-8*x*exp(2)^3+24*x^2*exp(2)^2-24*x^3*exp(2)+8*x^4)*exp(x)-4*e xp(2)^3+12*x*exp(2)^2-12*x^2*exp(2)+4*x^3)*exp(exp(x))^2+((-32*x*exp(2)^3+ 100*x^2*exp(2)^2-104*x^3*exp(2)+36*x^4)*exp(x)-32*exp(2)^3+104*x*exp(2)^2- 108*x^2*exp(2)+36*x^3)*exp(exp(x))-64*exp(2)^3+224*x*exp(2)^2-243*x^2*exp( 2)+81*x^3)/(4*exp(2)^3-12*x*exp(2)^2+12*x^2*exp(2)-4*x^3),x, algorithm="fr icas")
Output:
-1/4*(81*x^3 - 162*x^2*e^2 + 100*x*e^4 + 4*(x^3 - 2*x^2*e^2 + x*e^4)*e^(2* e^x) + 4*(9*x^3 - 17*x^2*e^2 + 8*x*e^4)*e^(e^x) - 18*e^6)/(x^2 - 2*x*e^2 + e^4)
Leaf count of result is larger than twice the leaf count of optimal. 70 vs. \(2 (22) = 44\).
Time = 0.21 (sec) , antiderivative size = 70, normalized size of antiderivative = 2.33 \[ \int \frac {-64 e^6+224 e^4 x-243 e^2 x^2+81 x^3+e^{2 e^x} \left (-4 e^6+12 e^4 x-12 e^2 x^2+4 x^3+e^x \left (-8 e^6 x+24 e^4 x^2-24 e^2 x^3+8 x^4\right )\right )+e^{e^x} \left (-32 e^6+104 e^4 x-108 e^2 x^2+36 x^3+e^x \left (-32 e^6 x+100 e^4 x^2-104 e^2 x^3+36 x^4\right )\right )}{4 e^6-12 e^4 x+12 e^2 x^2-4 x^3} \, dx=- \frac {81 x}{4} - \frac {19 x e^{4} - 18 e^{6}}{4 x^{2} - 8 x e^{2} + 4 e^{4}} + \frac {\left (- 9 x^{2} + 8 x e^{2}\right ) e^{e^{x}} + \left (- x^{2} + x e^{2}\right ) e^{2 e^{x}}}{x - e^{2}} \] Input:
integrate((((-8*x*exp(2)**3+24*x**2*exp(2)**2-24*x**3*exp(2)+8*x**4)*exp(x )-4*exp(2)**3+12*x*exp(2)**2-12*x**2*exp(2)+4*x**3)*exp(exp(x))**2+((-32*x *exp(2)**3+100*x**2*exp(2)**2-104*x**3*exp(2)+36*x**4)*exp(x)-32*exp(2)**3 +104*x*exp(2)**2-108*x**2*exp(2)+36*x**3)*exp(exp(x))-64*exp(2)**3+224*x*e xp(2)**2-243*x**2*exp(2)+81*x**3)/(4*exp(2)**3-12*x*exp(2)**2+12*x**2*exp( 2)-4*x**3),x)
Output:
-81*x/4 - (19*x*exp(4) - 18*exp(6))/(4*x**2 - 8*x*exp(2) + 4*exp(4)) + ((- 9*x**2 + 8*x*exp(2))*exp(exp(x)) + (-x**2 + x*exp(2))*exp(2*exp(x)))/(x - exp(2))
Leaf count of result is larger than twice the leaf count of optimal. 161 vs. \(2 (24) = 48\).
Time = 0.09 (sec) , antiderivative size = 161, normalized size of antiderivative = 5.37 \[ \int \frac {-64 e^6+224 e^4 x-243 e^2 x^2+81 x^3+e^{2 e^x} \left (-4 e^6+12 e^4 x-12 e^2 x^2+4 x^3+e^x \left (-8 e^6 x+24 e^4 x^2-24 e^2 x^3+8 x^4\right )\right )+e^{e^x} \left (-32 e^6+104 e^4 x-108 e^2 x^2+36 x^3+e^x \left (-32 e^6 x+100 e^4 x^2-104 e^2 x^3+36 x^4\right )\right )}{4 e^6-12 e^4 x+12 e^2 x^2-4 x^3} \, dx=-\frac {243}{8} \, {\left (\frac {4 \, x e^{2} - 3 \, e^{4}}{x^{2} - 2 \, x e^{2} + e^{4}} - 2 \, \log \left (x - e^{2}\right )\right )} e^{2} - \frac {243}{4} \, e^{2} \log \left (x - e^{2}\right ) - \frac {81}{4} \, x + \frac {28 \, {\left (2 \, x - e^{2}\right )} e^{4}}{x^{2} - 2 \, x e^{2} + e^{4}} + \frac {81 \, {\left (6 \, x e^{4} - 5 \, e^{6}\right )}}{8 \, {\left (x^{2} - 2 \, x e^{2} + e^{4}\right )}} - \frac {{\left (x^{2} - x e^{2}\right )} e^{\left (2 \, e^{x}\right )} + {\left (9 \, x^{2} - 8 \, x e^{2}\right )} e^{\left (e^{x}\right )}}{x - e^{2}} - \frac {8 \, e^{6}}{x^{2} - 2 \, x e^{2} + e^{4}} \] Input:
integrate((((-8*x*exp(2)^3+24*x^2*exp(2)^2-24*x^3*exp(2)+8*x^4)*exp(x)-4*e xp(2)^3+12*x*exp(2)^2-12*x^2*exp(2)+4*x^3)*exp(exp(x))^2+((-32*x*exp(2)^3+ 100*x^2*exp(2)^2-104*x^3*exp(2)+36*x^4)*exp(x)-32*exp(2)^3+104*x*exp(2)^2- 108*x^2*exp(2)+36*x^3)*exp(exp(x))-64*exp(2)^3+224*x*exp(2)^2-243*x^2*exp( 2)+81*x^3)/(4*exp(2)^3-12*x*exp(2)^2+12*x^2*exp(2)-4*x^3),x, algorithm="ma xima")
Output:
-243/8*((4*x*e^2 - 3*e^4)/(x^2 - 2*x*e^2 + e^4) - 2*log(x - e^2))*e^2 - 24 3/4*e^2*log(x - e^2) - 81/4*x + 28*(2*x - e^2)*e^4/(x^2 - 2*x*e^2 + e^4) + 81/8*(6*x*e^4 - 5*e^6)/(x^2 - 2*x*e^2 + e^4) - ((x^2 - x*e^2)*e^(2*e^x) + (9*x^2 - 8*x*e^2)*e^(e^x))/(x - e^2) - 8*e^6/(x^2 - 2*x*e^2 + e^4)
Leaf count of result is larger than twice the leaf count of optimal. 95 vs. \(2 (24) = 48\).
Time = 0.14 (sec) , antiderivative size = 95, normalized size of antiderivative = 3.17 \[ \int \frac {-64 e^6+224 e^4 x-243 e^2 x^2+81 x^3+e^{2 e^x} \left (-4 e^6+12 e^4 x-12 e^2 x^2+4 x^3+e^x \left (-8 e^6 x+24 e^4 x^2-24 e^2 x^3+8 x^4\right )\right )+e^{e^x} \left (-32 e^6+104 e^4 x-108 e^2 x^2+36 x^3+e^x \left (-32 e^6 x+100 e^4 x^2-104 e^2 x^3+36 x^4\right )\right )}{4 e^6-12 e^4 x+12 e^2 x^2-4 x^3} \, dx=-\frac {4 \, x^{3} e^{\left (2 \, e^{x}\right )} + 36 \, x^{3} e^{\left (e^{x}\right )} + 81 \, x^{3} - 162 \, x^{2} e^{2} - 8 \, x^{2} e^{\left (2 \, e^{x} + 2\right )} - 68 \, x^{2} e^{\left (e^{x} + 2\right )} + 100 \, x e^{4} + 4 \, x e^{\left (2 \, e^{x} + 4\right )} + 32 \, x e^{\left (e^{x} + 4\right )} - 18 \, e^{6}}{4 \, {\left (x^{2} - 2 \, x e^{2} + e^{4}\right )}} \] Input:
integrate((((-8*x*exp(2)^3+24*x^2*exp(2)^2-24*x^3*exp(2)+8*x^4)*exp(x)-4*e xp(2)^3+12*x*exp(2)^2-12*x^2*exp(2)+4*x^3)*exp(exp(x))^2+((-32*x*exp(2)^3+ 100*x^2*exp(2)^2-104*x^3*exp(2)+36*x^4)*exp(x)-32*exp(2)^3+104*x*exp(2)^2- 108*x^2*exp(2)+36*x^3)*exp(exp(x))-64*exp(2)^3+224*x*exp(2)^2-243*x^2*exp( 2)+81*x^3)/(4*exp(2)^3-12*x*exp(2)^2+12*x^2*exp(2)-4*x^3),x, algorithm="gi ac")
Output:
-1/4*(4*x^3*e^(2*e^x) + 36*x^3*e^(e^x) + 81*x^3 - 162*x^2*e^2 - 8*x^2*e^(2 *e^x + 2) - 68*x^2*e^(e^x + 2) + 100*x*e^4 + 4*x*e^(2*e^x + 4) + 32*x*e^(e ^x + 4) - 18*e^6)/(x^2 - 2*x*e^2 + e^4)
Time = 3.35 (sec) , antiderivative size = 63, normalized size of antiderivative = 2.10 \[ \int \frac {-64 e^6+224 e^4 x-243 e^2 x^2+81 x^3+e^{2 e^x} \left (-4 e^6+12 e^4 x-12 e^2 x^2+4 x^3+e^x \left (-8 e^6 x+24 e^4 x^2-24 e^2 x^3+8 x^4\right )\right )+e^{e^x} \left (-32 e^6+104 e^4 x-108 e^2 x^2+36 x^3+e^x \left (-32 e^6 x+100 e^4 x^2-104 e^2 x^3+36 x^4\right )\right )}{4 e^6-12 e^4 x+12 e^2 x^2-4 x^3} \, dx=\frac {18\,{\mathrm {e}}^6-19\,x\,{\mathrm {e}}^4}{4\,x^2-8\,{\mathrm {e}}^2\,x+4\,{\mathrm {e}}^4}-x\,{\mathrm {e}}^{2\,{\mathrm {e}}^x}-\frac {81\,x}{4}+\frac {{\mathrm {e}}^{{\mathrm {e}}^x}\,\left (8\,x\,{\mathrm {e}}^2-9\,x^2\right )}{x-{\mathrm {e}}^2} \] Input:
int(-(64*exp(6) + exp(exp(x))*(32*exp(6) - 104*x*exp(4) + exp(x)*(32*x*exp (6) + 104*x^3*exp(2) - 100*x^2*exp(4) - 36*x^4) + 108*x^2*exp(2) - 36*x^3) - 224*x*exp(4) + exp(2*exp(x))*(4*exp(6) - 12*x*exp(4) + exp(x)*(8*x*exp( 6) + 24*x^3*exp(2) - 24*x^2*exp(4) - 8*x^4) + 12*x^2*exp(2) - 4*x^3) + 243 *x^2*exp(2) - 81*x^3)/(4*exp(6) - 12*x*exp(4) + 12*x^2*exp(2) - 4*x^3),x)
Output:
(18*exp(6) - 19*x*exp(4))/(4*exp(4) - 8*x*exp(2) + 4*x^2) - x*exp(2*exp(x) ) - (81*x)/4 + (exp(exp(x))*(8*x*exp(2) - 9*x^2))/(x - exp(2))
Time = 0.16 (sec) , antiderivative size = 113, normalized size of antiderivative = 3.77 \[ \int \frac {-64 e^6+224 e^4 x-243 e^2 x^2+81 x^3+e^{2 e^x} \left (-4 e^6+12 e^4 x-12 e^2 x^2+4 x^3+e^x \left (-8 e^6 x+24 e^4 x^2-24 e^2 x^3+8 x^4\right )\right )+e^{e^x} \left (-32 e^6+104 e^4 x-108 e^2 x^2+36 x^3+e^x \left (-32 e^6 x+100 e^4 x^2-104 e^2 x^3+36 x^4\right )\right )}{4 e^6-12 e^4 x+12 e^2 x^2-4 x^3} \, dx=\frac {-4 e^{2 e^{x}} e^{4} x +8 e^{2 e^{x}} e^{2} x^{2}-4 e^{2 e^{x}} x^{3}-32 e^{e^{x}} e^{4} x +68 e^{e^{x}} e^{2} x^{2}-36 e^{e^{x}} x^{3}-32 e^{6}+112 e^{2} x^{2}-81 x^{3}}{4 e^{4}-8 e^{2} x +4 x^{2}} \] Input:
int((((-8*x*exp(2)^3+24*x^2*exp(2)^2-24*x^3*exp(2)+8*x^4)*exp(x)-4*exp(2)^ 3+12*x*exp(2)^2-12*x^2*exp(2)+4*x^3)*exp(exp(x))^2+((-32*x*exp(2)^3+100*x^ 2*exp(2)^2-104*x^3*exp(2)+36*x^4)*exp(x)-32*exp(2)^3+104*x*exp(2)^2-108*x^ 2*exp(2)+36*x^3)*exp(exp(x))-64*exp(2)^3+224*x*exp(2)^2-243*x^2*exp(2)+81* x^3)/(4*exp(2)^3-12*x*exp(2)^2+12*x^2*exp(2)-4*x^3),x)
Output:
( - 4*e**(2*e**x)*e**4*x + 8*e**(2*e**x)*e**2*x**2 - 4*e**(2*e**x)*x**3 - 32*e**(e**x)*e**4*x + 68*e**(e**x)*e**2*x**2 - 36*e**(e**x)*x**3 - 32*e**6 + 112*e**2*x**2 - 81*x**3)/(4*(e**4 - 2*e**2*x + x**2))