Integrand size = 436, antiderivative size = 36 \[ \int \left (-1+32 x-24 x^2+4 x^3+e^{2 x^2} \left (-8+66 x-32 x^2+4 x^3\right )+e^{x^2} \left (32-32 x+70 x^2-32 x^3+4 x^4\right )+e^{3 e^{2 x}-3 x} \left (e^{2 x^2} \left (24-48 e^{2 x}-32 x\right )-16 x+24 x^2-48 e^{2 x} x^2+e^{x^2} \left (-16+48 x-96 e^{2 x} x-32 x^2\right )\right )+e^{4 e^{2 x}-4 x} \left (2 x-4 x^2+8 e^{2 x} x^2+e^{2 x^2} \left (-4+8 e^{2 x}+4 x\right )+e^{x^2} \left (2-8 x+16 e^{2 x} x+4 x^2\right )\right )+e^{2 e^{2 x}-2 x} \left (48 x-54 x^2+4 x^3+e^{2 x^2} \left (-50+e^{2 x} (96-8 x)+100 x-8 x^2\right )+e^{2 x} \left (96 x^2-8 x^3\right )+e^{x^2} \left (48-104 x+104 x^2-8 x^3+e^{2 x} \left (192 x-16 x^2\right )\right )\right )+e^{e^{2 x}-x} \left (-64 x+56 x^2-8 x^3+e^{2 x} \left (-64 x^2+16 x^3\right )+e^{2 x^2} \left (40-136 x+32 x^2+e^{2 x} (-64+16 x)\right )+e^{x^2} \left (-64+96 x-144 x^2+32 x^3+e^{2 x} \left (-128 x+32 x^2\right )\right )\right )\right ) \, dx=-2-x+\left (e^{x^2}+x\right )^2 \left (-\left (-2+e^{e^{2 x}-x}\right )^2+x\right )^2 \]
Leaf count is larger than twice the leaf count of optimal. \(321\) vs. \(2(36)=72\).
Time = 16.80 (sec) , antiderivative size = 321, normalized size of antiderivative = 8.92 \[ \int \left (-1+32 x-24 x^2+4 x^3+e^{2 x^2} \left (-8+66 x-32 x^2+4 x^3\right )+e^{x^2} \left (32-32 x+70 x^2-32 x^3+4 x^4\right )+e^{3 e^{2 x}-3 x} \left (e^{2 x^2} \left (24-48 e^{2 x}-32 x\right )-16 x+24 x^2-48 e^{2 x} x^2+e^{x^2} \left (-16+48 x-96 e^{2 x} x-32 x^2\right )\right )+e^{4 e^{2 x}-4 x} \left (2 x-4 x^2+8 e^{2 x} x^2+e^{2 x^2} \left (-4+8 e^{2 x}+4 x\right )+e^{x^2} \left (2-8 x+16 e^{2 x} x+4 x^2\right )\right )+e^{2 e^{2 x}-2 x} \left (48 x-54 x^2+4 x^3+e^{2 x^2} \left (-50+e^{2 x} (96-8 x)+100 x-8 x^2\right )+e^{2 x} \left (96 x^2-8 x^3\right )+e^{x^2} \left (48-104 x+104 x^2-8 x^3+e^{2 x} \left (192 x-16 x^2\right )\right )\right )+e^{e^{2 x}-x} \left (-64 x+56 x^2-8 x^3+e^{2 x} \left (-64 x^2+16 x^3\right )+e^{2 x^2} \left (40-136 x+32 x^2+e^{2 x} (-64+16 x)\right )+e^{x^2} \left (-64+96 x-144 x^2+32 x^3+e^{2 x} \left (-128 x+32 x^2\right )\right )\right )\right ) \, dx=16 e^{2 x^2}-x+32 e^{x^2} x-8 e^{2 x^2} x+16 x^2-16 e^{x^2} x^2+e^{2 x^2} x^2-8 x^3+2 e^{x^2} x^3+x^4+\frac {2 e^{4 e^{2 x}-4 x} \left (e^{x^2}+x\right ) \left (-2 e^{x^2}+4 e^{2 x+x^2}-2 x+4 e^{2 x} x\right )}{-4+8 e^{2 x}}-\frac {8 e^{3 e^{2 x}-3 x} \left (e^{x^2}+x\right ) \left (-3 e^{x^2}+6 e^{2 x+x^2}-3 x+6 e^{2 x} x\right )}{-3+6 e^{2 x}}-2 e^{2 e^{2 x}} \left (e^{-2 x+2 x^2} (-12+x)+e^{-2 x+x^2} \left (-24 x+2 x^2\right )+e^{-2 x} \left (-12 x^2+x^3\right )\right )+8 e^{e^{2 x}} \left (e^{-x+2 x^2} (-4+x)+e^{-x+x^2} \left (-8 x+2 x^2\right )+e^{-x} \left (-4 x^2+x^3\right )\right ) \]
Integrate[-1 + 32*x - 24*x^2 + 4*x^3 + E^(2*x^2)*(-8 + 66*x - 32*x^2 + 4*x ^3) + E^x^2*(32 - 32*x + 70*x^2 - 32*x^3 + 4*x^4) + E^(3*E^(2*x) - 3*x)*(E ^(2*x^2)*(24 - 48*E^(2*x) - 32*x) - 16*x + 24*x^2 - 48*E^(2*x)*x^2 + E^x^2 *(-16 + 48*x - 96*E^(2*x)*x - 32*x^2)) + E^(4*E^(2*x) - 4*x)*(2*x - 4*x^2 + 8*E^(2*x)*x^2 + E^(2*x^2)*(-4 + 8*E^(2*x) + 4*x) + E^x^2*(2 - 8*x + 16*E ^(2*x)*x + 4*x^2)) + E^(2*E^(2*x) - 2*x)*(48*x - 54*x^2 + 4*x^3 + E^(2*x^2 )*(-50 + E^(2*x)*(96 - 8*x) + 100*x - 8*x^2) + E^(2*x)*(96*x^2 - 8*x^3) + E^x^2*(48 - 104*x + 104*x^2 - 8*x^3 + E^(2*x)*(192*x - 16*x^2))) + E^(E^(2 *x) - x)*(-64*x + 56*x^2 - 8*x^3 + E^(2*x)*(-64*x^2 + 16*x^3) + E^(2*x^2)* (40 - 136*x + 32*x^2 + E^(2*x)*(-64 + 16*x)) + E^x^2*(-64 + 96*x - 144*x^2 + 32*x^3 + E^(2*x)*(-128*x + 32*x^2))),x]
16*E^(2*x^2) - x + 32*E^x^2*x - 8*E^(2*x^2)*x + 16*x^2 - 16*E^x^2*x^2 + E^ (2*x^2)*x^2 - 8*x^3 + 2*E^x^2*x^3 + x^4 + (2*E^(4*E^(2*x) - 4*x)*(E^x^2 + x)*(-2*E^x^2 + 4*E^(2*x + x^2) - 2*x + 4*E^(2*x)*x))/(-4 + 8*E^(2*x)) - (8 *E^(3*E^(2*x) - 3*x)*(E^x^2 + x)*(-3*E^x^2 + 6*E^(2*x + x^2) - 3*x + 6*E^( 2*x)*x))/(-3 + 6*E^(2*x)) - 2*E^(2*E^(2*x))*(E^(-2*x + 2*x^2)*(-12 + x) + E^(-2*x + x^2)*(-24*x + 2*x^2) + (-12*x^2 + x^3)/E^(2*x)) + 8*E^E^(2*x)*(E ^(-x + 2*x^2)*(-4 + x) + E^(-x + x^2)*(-8*x + 2*x^2) + (-4*x^2 + x^3)/E^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.
| \(\displaystyle \int \left (4 x^3-24 x^2+e^{3 e^{2 x}-3 x} \left (-48 e^{2 x} x^2+24 x^2+e^{2 x^2} \left (-32 x-48 e^{2 x}+24\right )+e^{x^2} \left (-32 x^2-96 e^{2 x} x+48 x-16\right )-16 x\right )+e^{4 e^{2 x}-4 x} \left (8 e^{2 x} x^2-4 x^2+e^{2 x^2} \left (4 x+8 e^{2 x}-4\right )+e^{x^2} \left (4 x^2+16 e^{2 x} x-8 x+2\right )+2 x\right )+e^{2 x^2} \left (4 x^3-32 x^2+66 x-8\right )+e^{2 e^{2 x}-2 x} \left (4 x^3-54 x^2+e^{2 x^2} \left (-8 x^2+100 x+e^{2 x} (96-8 x)-50\right )+e^{2 x} \left (96 x^2-8 x^3\right )+e^{x^2} \left (-8 x^3+104 x^2+e^{2 x} \left (192 x-16 x^2\right )-104 x+48\right )+48 x\right )+e^{e^{2 x}-x} \left (-8 x^3+56 x^2+e^{2 x^2} \left (32 x^2-136 x+e^{2 x} (16 x-64)+40\right )+e^{2 x} \left (16 x^3-64 x^2\right )+e^{x^2} \left (32 x^3-144 x^2+e^{2 x} \left (32 x^2-128 x\right )+96 x-64\right )-64 x\right )+e^{x^2} \left (4 x^4-32 x^3+70 x^2-32 x+32\right )+32 x-1\right ) \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \left (4 x^3-24 x^2+2 e^{4 \left (e^{2 x}-x\right )} \left (e^{x^2}+x\right ) \left (2 e^{x^2} x-2 e^{x^2}+4 e^{2 x} x-2 x+4 e^{x (x+2)}+1\right )-8 e^{3 \left (e^{2 x}-x\right )} \left (e^{x^2}+x\right ) \left (4 e^{x^2} x-3 e^{x^2}+6 e^{2 x} x-3 x+6 e^{x (x+2)}+2\right )+8 e^{e^{2 x}-x} \left (e^{x^2}+x\right ) \left (4 e^{x^2} x^2+2 e^{2 x} x^2-x^2-17 e^{x^2} x+5 e^{x^2}-8 e^{2 x} x+2 e^{x (x+2)} x+7 x-8 e^{x (x+2)}-8\right )-2 e^{2 \left (e^{2 x}-x\right )} \left (e^{x^2}+x\right ) \left (4 e^{x^2} x^2+4 e^{2 x} x^2-2 x^2-50 e^{x^2} x+25 e^{x^2}-48 e^{2 x} x+4 e^{x (x+2)} x+27 x-48 e^{x (x+2)}-24\right )+e^{2 x^2} \left (4 x^3-32 x^2+66 x-8\right )+e^{x^2} \left (4 x^4-32 x^3+70 x^2-32 x+32\right )+32 x-1\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (4 x^3-24 x^2+8 e^{3 \left (e^{2 x}-x\right )} \left (e^{x^2}+x\right ) \left (-4 e^{x^2} x+3 e^{x^2}-6 e^{2 x} x+3 x-6 e^{x (x+2)}-2\right )+2 e^{4 \left (e^{2 x}-x\right )} \left (e^{x^2}+x\right ) \left (2 e^{x^2} x-2 e^{x^2}+4 e^{2 x} x-2 x+4 e^{x (x+2)}+1\right )+2 e^{2 \left (e^{2 x}-x\right )} \left (e^{x^2}+x\right ) \left (-4 e^{x^2} x^2-4 e^{2 x} x^2+2 x^2+50 e^{x^2} x-25 e^{x^2}+48 e^{2 x} x-4 e^{x (x+2)} x-27 x+48 e^{x (x+2)}+24\right )+8 e^{e^{2 x}-x} \left (e^{x^2}+x\right ) \left (4 e^{x^2} x^2+2 e^{2 x} x^2-x^2-17 e^{x^2} x+5 e^{x^2}-8 e^{2 x} x+2 e^{x (x+2)} x+7 x-8 e^{x (x+2)}-8\right )+2 e^{2 x^2} \left (2 x^3-16 x^2+33 x-4\right )+2 e^{x^2} \left (2 x^4-16 x^3+35 x^2-16 x+16\right )+32 x-1\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle \int \left (4 x^3-24 x^2+8 e^{3 \left (e^{2 x}-x\right )} \left (e^{x^2}+x\right ) \left (-4 e^{x^2} x+3 e^{x^2}-6 e^{2 x} x+3 x-6 e^{x (x+2)}-2\right )+2 e^{4 \left (e^{2 x}-x\right )} \left (e^{x^2}+x\right ) \left (2 e^{x^2} x-2 e^{x^2}+4 e^{2 x} x-2 x+4 e^{x (x+2)}+1\right )+2 e^{2 \left (e^{2 x}-x\right )} \left (e^{x^2}+x\right ) \left (-4 e^{x^2} x^2-4 e^{2 x} x^2+2 x^2+50 e^{x^2} x-25 e^{x^2}+48 e^{2 x} x-4 e^{x (x+2)} x-27 x+48 e^{x (x+2)}+24\right )+8 e^{e^{2 x}-x} \left (e^{x^2}+x\right ) \left (4 e^{x^2} x^2+2 e^{2 x} x^2-x^2-17 e^{x^2} x+5 e^{x^2}-8 e^{2 x} x+2 e^{x (x+2)} x+7 x-8 e^{x (x+2)}-8\right )+2 e^{2 x^2} \left (2 x^3-16 x^2+33 x-4\right )+2 e^{x^2} \left (2 x^4-16 x^3+35 x^2-16 x+16\right )+32 x-1\right )dx\) |
Int[-1 + 32*x - 24*x^2 + 4*x^3 + E^(2*x^2)*(-8 + 66*x - 32*x^2 + 4*x^3) + E^x^2*(32 - 32*x + 70*x^2 - 32*x^3 + 4*x^4) + E^(3*E^(2*x) - 3*x)*(E^(2*x^ 2)*(24 - 48*E^(2*x) - 32*x) - 16*x + 24*x^2 - 48*E^(2*x)*x^2 + E^x^2*(-16 + 48*x - 96*E^(2*x)*x - 32*x^2)) + E^(4*E^(2*x) - 4*x)*(2*x - 4*x^2 + 8*E^ (2*x)*x^2 + E^(2*x^2)*(-4 + 8*E^(2*x) + 4*x) + E^x^2*(2 - 8*x + 16*E^(2*x) *x + 4*x^2)) + E^(2*E^(2*x) - 2*x)*(48*x - 54*x^2 + 4*x^3 + E^(2*x^2)*(-50 + E^(2*x)*(96 - 8*x) + 100*x - 8*x^2) + E^(2*x)*(96*x^2 - 8*x^3) + E^x^2* (48 - 104*x + 104*x^2 - 8*x^3 + E^(2*x)*(192*x - 16*x^2))) + E^(E^(2*x) - x)*(-64*x + 56*x^2 - 8*x^3 + E^(2*x)*(-64*x^2 + 16*x^3) + E^(2*x^2)*(40 - 136*x + 32*x^2 + E^(2*x)*(-64 + 16*x)) + E^x^2*(-64 + 96*x - 144*x^2 + 32* x^3 + E^(2*x)*(-128*x + 32*x^2))),x]
3.15.43.3.1 Defintions of rubi rules used
Leaf count of result is larger than twice the leaf count of optimal. \(223\) vs. \(2(33)=66\).
Time = 0.44 (sec) , antiderivative size = 224, normalized size of antiderivative = 6.22
| method | result | size |
| risch | \(\left (x^{2}+2 \,{\mathrm e}^{x^{2}} x +{\mathrm e}^{2 x^{2}}\right ) {\mathrm e}^{4 \,{\mathrm e}^{2 x}-4 x}+\left (-8 x^{2}-16 \,{\mathrm e}^{x^{2}} x -8 \,{\mathrm e}^{2 x^{2}}\right ) {\mathrm e}^{3 \,{\mathrm e}^{2 x}-3 x}+\left (-2 x^{3}-4 x^{2} {\mathrm e}^{x^{2}}-2 x \,{\mathrm e}^{2 x^{2}}+24 x^{2}+48 \,{\mathrm e}^{x^{2}} x +24 \,{\mathrm e}^{2 x^{2}}\right ) {\mathrm e}^{2 \,{\mathrm e}^{2 x}-2 x}+\left (8 x^{3}+16 x^{2} {\mathrm e}^{x^{2}}+8 x \,{\mathrm e}^{2 x^{2}}-32 x^{2}-64 \,{\mathrm e}^{x^{2}} x -32 \,{\mathrm e}^{2 x^{2}}\right ) {\mathrm e}^{{\mathrm e}^{2 x}-x}+\left (x^{2}-8 x +16\right ) {\mathrm e}^{2 x^{2}}+\left (2 x^{3}-16 x^{2}+32 x \right ) {\mathrm e}^{x^{2}}+x^{4}-8 x^{3}+16 x^{2}-x\) | \(224\) |
| parallelrisch | \(-x +{\mathrm e}^{2 x^{2}} x^{2}+2 x^{3} {\mathrm e}^{x^{2}}-8 x \,{\mathrm e}^{2 x^{2}}+32 \,{\mathrm e}^{x^{2}} x +16 \,{\mathrm e}^{2 x^{2}}+x^{4}-8 x^{3}+16 x^{2}-16 x^{2} {\mathrm e}^{x^{2}}+2 \,{\mathrm e}^{x^{2}} {\mathrm e}^{4 \,{\mathrm e}^{2 x}-4 x} x -16 \,{\mathrm e}^{x^{2}} {\mathrm e}^{3 \,{\mathrm e}^{2 x}-3 x} x +48 \,{\mathrm e}^{x^{2}} {\mathrm e}^{2 \,{\mathrm e}^{2 x}-2 x} x -64 \,{\mathrm e}^{x^{2}} {\mathrm e}^{{\mathrm e}^{2 x}-x} x -2 \,{\mathrm e}^{2 x^{2}} {\mathrm e}^{2 \,{\mathrm e}^{2 x}-2 x} x +8 \,{\mathrm e}^{2 x^{2}} {\mathrm e}^{{\mathrm e}^{2 x}-x} x -4 \,{\mathrm e}^{x^{2}} {\mathrm e}^{2 \,{\mathrm e}^{2 x}-2 x} x^{2}+16 \,{\mathrm e}^{x^{2}} {\mathrm e}^{{\mathrm e}^{2 x}-x} x^{2}-2 \,{\mathrm e}^{2 \,{\mathrm e}^{2 x}-2 x} x^{3}+8 \,{\mathrm e}^{{\mathrm e}^{2 x}-x} x^{3}+{\mathrm e}^{4 \,{\mathrm e}^{2 x}-4 x} x^{2}-8 \,{\mathrm e}^{3 \,{\mathrm e}^{2 x}-3 x} x^{2}+24 \,{\mathrm e}^{2 \,{\mathrm e}^{2 x}-2 x} x^{2}-32 \,{\mathrm e}^{{\mathrm e}^{2 x}-x} x^{2}+{\mathrm e}^{2 x^{2}} {\mathrm e}^{4 \,{\mathrm e}^{2 x}-4 x}-8 \,{\mathrm e}^{2 x^{2}} {\mathrm e}^{3 \,{\mathrm e}^{2 x}-3 x}+24 \,{\mathrm e}^{2 x^{2}} {\mathrm e}^{2 \,{\mathrm e}^{2 x}-2 x}-32 \,{\mathrm e}^{2 x^{2}} {\mathrm e}^{{\mathrm e}^{2 x}-x}\) | \(380\) |
int(((8*exp(x)^2+4*x-4)*exp(x^2)^2+(16*x*exp(x)^2+4*x^2-8*x+2)*exp(x^2)+8* exp(x)^2*x^2-4*x^2+2*x)*exp(exp(x)^2-x)^4+((-48*exp(x)^2-32*x+24)*exp(x^2) ^2+(-96*x*exp(x)^2-32*x^2+48*x-16)*exp(x^2)-48*exp(x)^2*x^2+24*x^2-16*x)*e xp(exp(x)^2-x)^3+(((-8*x+96)*exp(x)^2-8*x^2+100*x-50)*exp(x^2)^2+((-16*x^2 +192*x)*exp(x)^2-8*x^3+104*x^2-104*x+48)*exp(x^2)+(-8*x^3+96*x^2)*exp(x)^2 +4*x^3-54*x^2+48*x)*exp(exp(x)^2-x)^2+(((16*x-64)*exp(x)^2+32*x^2-136*x+40 )*exp(x^2)^2+((32*x^2-128*x)*exp(x)^2+32*x^3-144*x^2+96*x-64)*exp(x^2)+(16 *x^3-64*x^2)*exp(x)^2-8*x^3+56*x^2-64*x)*exp(exp(x)^2-x)+(4*x^3-32*x^2+66* x-8)*exp(x^2)^2+(4*x^4-32*x^3+70*x^2-32*x+32)*exp(x^2)+4*x^3-24*x^2+32*x-1 ,x,method=_RETURNVERBOSE)
(x^2+2*exp(x^2)*x+exp(2*x^2))*exp(4*exp(2*x)-4*x)+(-8*x^2-16*exp(x^2)*x-8* exp(2*x^2))*exp(3*exp(2*x)-3*x)+(-2*x^3-4*x^2*exp(x^2)-2*x*exp(2*x^2)+24*x ^2+48*exp(x^2)*x+24*exp(2*x^2))*exp(2*exp(2*x)-2*x)+(8*x^3+16*x^2*exp(x^2) +8*x*exp(2*x^2)-32*x^2-64*exp(x^2)*x-32*exp(2*x^2))*exp(exp(2*x)-x)+(x^2-8 *x+16)*exp(2*x^2)+(2*x^3-16*x^2+32*x)*exp(x^2)+x^4-8*x^3+16*x^2-x
Leaf count of result is larger than twice the leaf count of optimal. 197 vs. \(2 (33) = 66\).
Time = 0.27 (sec) , antiderivative size = 197, normalized size of antiderivative = 5.47 \[ \int \left (-1+32 x-24 x^2+4 x^3+e^{2 x^2} \left (-8+66 x-32 x^2+4 x^3\right )+e^{x^2} \left (32-32 x+70 x^2-32 x^3+4 x^4\right )+e^{3 e^{2 x}-3 x} \left (e^{2 x^2} \left (24-48 e^{2 x}-32 x\right )-16 x+24 x^2-48 e^{2 x} x^2+e^{x^2} \left (-16+48 x-96 e^{2 x} x-32 x^2\right )\right )+e^{4 e^{2 x}-4 x} \left (2 x-4 x^2+8 e^{2 x} x^2+e^{2 x^2} \left (-4+8 e^{2 x}+4 x\right )+e^{x^2} \left (2-8 x+16 e^{2 x} x+4 x^2\right )\right )+e^{2 e^{2 x}-2 x} \left (48 x-54 x^2+4 x^3+e^{2 x^2} \left (-50+e^{2 x} (96-8 x)+100 x-8 x^2\right )+e^{2 x} \left (96 x^2-8 x^3\right )+e^{x^2} \left (48-104 x+104 x^2-8 x^3+e^{2 x} \left (192 x-16 x^2\right )\right )\right )+e^{e^{2 x}-x} \left (-64 x+56 x^2-8 x^3+e^{2 x} \left (-64 x^2+16 x^3\right )+e^{2 x^2} \left (40-136 x+32 x^2+e^{2 x} (-64+16 x)\right )+e^{x^2} \left (-64+96 x-144 x^2+32 x^3+e^{2 x} \left (-128 x+32 x^2\right )\right )\right )\right ) \, dx=x^{4} - 8 \, x^{3} + 16 \, x^{2} + {\left (x^{2} - 8 \, x + 16\right )} e^{\left (2 \, x^{2}\right )} + 2 \, {\left (x^{3} - 8 \, x^{2} + 16 \, x\right )} e^{\left (x^{2}\right )} + 8 \, {\left (x^{3} - 4 \, x^{2} + {\left (x - 4\right )} e^{\left (2 \, x^{2}\right )} + 2 \, {\left (x^{2} - 4 \, x\right )} e^{\left (x^{2}\right )}\right )} e^{\left (-x + e^{\left (2 \, x\right )}\right )} - 2 \, {\left (x^{3} - 12 \, x^{2} + {\left (x - 12\right )} e^{\left (2 \, x^{2}\right )} + 2 \, {\left (x^{2} - 12 \, x\right )} e^{\left (x^{2}\right )}\right )} e^{\left (-2 \, x + 2 \, e^{\left (2 \, x\right )}\right )} - 8 \, {\left (x^{2} + 2 \, x e^{\left (x^{2}\right )} + e^{\left (2 \, x^{2}\right )}\right )} e^{\left (-3 \, x + 3 \, e^{\left (2 \, x\right )}\right )} + {\left (x^{2} + 2 \, x e^{\left (x^{2}\right )} + e^{\left (2 \, x^{2}\right )}\right )} e^{\left (-4 \, x + 4 \, e^{\left (2 \, x\right )}\right )} - x \]
integrate(((8*exp(x)^2+4*x-4)*exp(x^2)^2+(16*x*exp(x)^2+4*x^2-8*x+2)*exp(x ^2)+8*exp(x)^2*x^2-4*x^2+2*x)*exp(exp(x)^2-x)^4+((-48*exp(x)^2-32*x+24)*ex p(x^2)^2+(-96*x*exp(x)^2-32*x^2+48*x-16)*exp(x^2)-48*exp(x)^2*x^2+24*x^2-1 6*x)*exp(exp(x)^2-x)^3+(((-8*x+96)*exp(x)^2-8*x^2+100*x-50)*exp(x^2)^2+((- 16*x^2+192*x)*exp(x)^2-8*x^3+104*x^2-104*x+48)*exp(x^2)+(-8*x^3+96*x^2)*ex p(x)^2+4*x^3-54*x^2+48*x)*exp(exp(x)^2-x)^2+(((16*x-64)*exp(x)^2+32*x^2-13 6*x+40)*exp(x^2)^2+((32*x^2-128*x)*exp(x)^2+32*x^3-144*x^2+96*x-64)*exp(x^ 2)+(16*x^3-64*x^2)*exp(x)^2-8*x^3+56*x^2-64*x)*exp(exp(x)^2-x)+(4*x^3-32*x ^2+66*x-8)*exp(x^2)^2+(4*x^4-32*x^3+70*x^2-32*x+32)*exp(x^2)+4*x^3-24*x^2+ 32*x-1,x, algorithm=\
x^4 - 8*x^3 + 16*x^2 + (x^2 - 8*x + 16)*e^(2*x^2) + 2*(x^3 - 8*x^2 + 16*x) *e^(x^2) + 8*(x^3 - 4*x^2 + (x - 4)*e^(2*x^2) + 2*(x^2 - 4*x)*e^(x^2))*e^( -x + e^(2*x)) - 2*(x^3 - 12*x^2 + (x - 12)*e^(2*x^2) + 2*(x^2 - 12*x)*e^(x ^2))*e^(-2*x + 2*e^(2*x)) - 8*(x^2 + 2*x*e^(x^2) + e^(2*x^2))*e^(-3*x + 3* e^(2*x)) + (x^2 + 2*x*e^(x^2) + e^(2*x^2))*e^(-4*x + 4*e^(2*x)) - x
Leaf count of result is larger than twice the leaf count of optimal. 230 vs. \(2 (26) = 52\).
Time = 2.45 (sec) , antiderivative size = 230, normalized size of antiderivative = 6.39 \[ \int \left (-1+32 x-24 x^2+4 x^3+e^{2 x^2} \left (-8+66 x-32 x^2+4 x^3\right )+e^{x^2} \left (32-32 x+70 x^2-32 x^3+4 x^4\right )+e^{3 e^{2 x}-3 x} \left (e^{2 x^2} \left (24-48 e^{2 x}-32 x\right )-16 x+24 x^2-48 e^{2 x} x^2+e^{x^2} \left (-16+48 x-96 e^{2 x} x-32 x^2\right )\right )+e^{4 e^{2 x}-4 x} \left (2 x-4 x^2+8 e^{2 x} x^2+e^{2 x^2} \left (-4+8 e^{2 x}+4 x\right )+e^{x^2} \left (2-8 x+16 e^{2 x} x+4 x^2\right )\right )+e^{2 e^{2 x}-2 x} \left (48 x-54 x^2+4 x^3+e^{2 x^2} \left (-50+e^{2 x} (96-8 x)+100 x-8 x^2\right )+e^{2 x} \left (96 x^2-8 x^3\right )+e^{x^2} \left (48-104 x+104 x^2-8 x^3+e^{2 x} \left (192 x-16 x^2\right )\right )\right )+e^{e^{2 x}-x} \left (-64 x+56 x^2-8 x^3+e^{2 x} \left (-64 x^2+16 x^3\right )+e^{2 x^2} \left (40-136 x+32 x^2+e^{2 x} (-64+16 x)\right )+e^{x^2} \left (-64+96 x-144 x^2+32 x^3+e^{2 x} \left (-128 x+32 x^2\right )\right )\right )\right ) \, dx=x^{4} - 8 x^{3} + 16 x^{2} - x + \left (- 8 x^{2} - 16 x e^{x^{2}} - 8 e^{2 x^{2}}\right ) e^{- 3 x + 3 e^{2 x}} + \left (x^{2} - 8 x + 16\right ) e^{2 x^{2}} + \left (x^{2} + 2 x e^{x^{2}} + e^{2 x^{2}}\right ) e^{- 4 x + 4 e^{2 x}} + \left (2 x^{3} - 16 x^{2} + 32 x\right ) e^{x^{2}} + \left (- 2 x^{3} - 4 x^{2} e^{x^{2}} + 24 x^{2} - 2 x e^{2 x^{2}} + 48 x e^{x^{2}} + 24 e^{2 x^{2}}\right ) e^{- 2 x + 2 e^{2 x}} + \left (8 x^{3} + 16 x^{2} e^{x^{2}} - 32 x^{2} + 8 x e^{2 x^{2}} - 64 x e^{x^{2}} - 32 e^{2 x^{2}}\right ) e^{- x + e^{2 x}} \]
integrate(((8*exp(x)**2+4*x-4)*exp(x**2)**2+(16*x*exp(x)**2+4*x**2-8*x+2)* exp(x**2)+8*exp(x)**2*x**2-4*x**2+2*x)*exp(exp(x)**2-x)**4+((-48*exp(x)**2 -32*x+24)*exp(x**2)**2+(-96*x*exp(x)**2-32*x**2+48*x-16)*exp(x**2)-48*exp( x)**2*x**2+24*x**2-16*x)*exp(exp(x)**2-x)**3+(((-8*x+96)*exp(x)**2-8*x**2+ 100*x-50)*exp(x**2)**2+((-16*x**2+192*x)*exp(x)**2-8*x**3+104*x**2-104*x+4 8)*exp(x**2)+(-8*x**3+96*x**2)*exp(x)**2+4*x**3-54*x**2+48*x)*exp(exp(x)** 2-x)**2+(((16*x-64)*exp(x)**2+32*x**2-136*x+40)*exp(x**2)**2+((32*x**2-128 *x)*exp(x)**2+32*x**3-144*x**2+96*x-64)*exp(x**2)+(16*x**3-64*x**2)*exp(x) **2-8*x**3+56*x**2-64*x)*exp(exp(x)**2-x)+(4*x**3-32*x**2+66*x-8)*exp(x**2 )**2+(4*x**4-32*x**3+70*x**2-32*x+32)*exp(x**2)+4*x**3-24*x**2+32*x-1,x)
x**4 - 8*x**3 + 16*x**2 - x + (-8*x**2 - 16*x*exp(x**2) - 8*exp(2*x**2))*e xp(-3*x + 3*exp(2*x)) + (x**2 - 8*x + 16)*exp(2*x**2) + (x**2 + 2*x*exp(x* *2) + exp(2*x**2))*exp(-4*x + 4*exp(2*x)) + (2*x**3 - 16*x**2 + 32*x)*exp( x**2) + (-2*x**3 - 4*x**2*exp(x**2) + 24*x**2 - 2*x*exp(2*x**2) + 48*x*exp (x**2) + 24*exp(2*x**2))*exp(-2*x + 2*exp(2*x)) + (8*x**3 + 16*x**2*exp(x* *2) - 32*x**2 + 8*x*exp(2*x**2) - 64*x*exp(x**2) - 32*exp(2*x**2))*exp(-x + exp(2*x))
Leaf count of result is larger than twice the leaf count of optimal. 197 vs. \(2 (33) = 66\).
Time = 0.22 (sec) , antiderivative size = 197, normalized size of antiderivative = 5.47 \[ \int \left (-1+32 x-24 x^2+4 x^3+e^{2 x^2} \left (-8+66 x-32 x^2+4 x^3\right )+e^{x^2} \left (32-32 x+70 x^2-32 x^3+4 x^4\right )+e^{3 e^{2 x}-3 x} \left (e^{2 x^2} \left (24-48 e^{2 x}-32 x\right )-16 x+24 x^2-48 e^{2 x} x^2+e^{x^2} \left (-16+48 x-96 e^{2 x} x-32 x^2\right )\right )+e^{4 e^{2 x}-4 x} \left (2 x-4 x^2+8 e^{2 x} x^2+e^{2 x^2} \left (-4+8 e^{2 x}+4 x\right )+e^{x^2} \left (2-8 x+16 e^{2 x} x+4 x^2\right )\right )+e^{2 e^{2 x}-2 x} \left (48 x-54 x^2+4 x^3+e^{2 x^2} \left (-50+e^{2 x} (96-8 x)+100 x-8 x^2\right )+e^{2 x} \left (96 x^2-8 x^3\right )+e^{x^2} \left (48-104 x+104 x^2-8 x^3+e^{2 x} \left (192 x-16 x^2\right )\right )\right )+e^{e^{2 x}-x} \left (-64 x+56 x^2-8 x^3+e^{2 x} \left (-64 x^2+16 x^3\right )+e^{2 x^2} \left (40-136 x+32 x^2+e^{2 x} (-64+16 x)\right )+e^{x^2} \left (-64+96 x-144 x^2+32 x^3+e^{2 x} \left (-128 x+32 x^2\right )\right )\right )\right ) \, dx=x^{4} - 8 \, x^{3} + 16 \, x^{2} + {\left (x^{2} - 8 \, x + 16\right )} e^{\left (2 \, x^{2}\right )} + 2 \, {\left (x^{3} - 8 \, x^{2} + 16 \, x\right )} e^{\left (x^{2}\right )} + 8 \, {\left (x^{3} - 4 \, x^{2} + {\left (x - 4\right )} e^{\left (2 \, x^{2}\right )} + 2 \, {\left (x^{2} - 4 \, x\right )} e^{\left (x^{2}\right )}\right )} e^{\left (-x + e^{\left (2 \, x\right )}\right )} - 2 \, {\left (x^{3} - 12 \, x^{2} + {\left (x - 12\right )} e^{\left (2 \, x^{2}\right )} + 2 \, {\left (x^{2} - 12 \, x\right )} e^{\left (x^{2}\right )}\right )} e^{\left (-2 \, x + 2 \, e^{\left (2 \, x\right )}\right )} - 8 \, {\left (x^{2} + 2 \, x e^{\left (x^{2}\right )} + e^{\left (2 \, x^{2}\right )}\right )} e^{\left (-3 \, x + 3 \, e^{\left (2 \, x\right )}\right )} + {\left (x^{2} + 2 \, x e^{\left (x^{2}\right )} + e^{\left (2 \, x^{2}\right )}\right )} e^{\left (-4 \, x + 4 \, e^{\left (2 \, x\right )}\right )} - x \]
integrate(((8*exp(x)^2+4*x-4)*exp(x^2)^2+(16*x*exp(x)^2+4*x^2-8*x+2)*exp(x ^2)+8*exp(x)^2*x^2-4*x^2+2*x)*exp(exp(x)^2-x)^4+((-48*exp(x)^2-32*x+24)*ex p(x^2)^2+(-96*x*exp(x)^2-32*x^2+48*x-16)*exp(x^2)-48*exp(x)^2*x^2+24*x^2-1 6*x)*exp(exp(x)^2-x)^3+(((-8*x+96)*exp(x)^2-8*x^2+100*x-50)*exp(x^2)^2+((- 16*x^2+192*x)*exp(x)^2-8*x^3+104*x^2-104*x+48)*exp(x^2)+(-8*x^3+96*x^2)*ex p(x)^2+4*x^3-54*x^2+48*x)*exp(exp(x)^2-x)^2+(((16*x-64)*exp(x)^2+32*x^2-13 6*x+40)*exp(x^2)^2+((32*x^2-128*x)*exp(x)^2+32*x^3-144*x^2+96*x-64)*exp(x^ 2)+(16*x^3-64*x^2)*exp(x)^2-8*x^3+56*x^2-64*x)*exp(exp(x)^2-x)+(4*x^3-32*x ^2+66*x-8)*exp(x^2)^2+(4*x^4-32*x^3+70*x^2-32*x+32)*exp(x^2)+4*x^3-24*x^2+ 32*x-1,x, algorithm=\
x^4 - 8*x^3 + 16*x^2 + (x^2 - 8*x + 16)*e^(2*x^2) + 2*(x^3 - 8*x^2 + 16*x) *e^(x^2) + 8*(x^3 - 4*x^2 + (x - 4)*e^(2*x^2) + 2*(x^2 - 4*x)*e^(x^2))*e^( -x + e^(2*x)) - 2*(x^3 - 12*x^2 + (x - 12)*e^(2*x^2) + 2*(x^2 - 12*x)*e^(x ^2))*e^(-2*x + 2*e^(2*x)) - 8*(x^2 + 2*x*e^(x^2) + e^(2*x^2))*e^(-3*x + 3* e^(2*x)) + (x^2 + 2*x*e^(x^2) + e^(2*x^2))*e^(-4*x + 4*e^(2*x)) - x
Leaf count of result is larger than twice the leaf count of optimal. 383 vs. \(2 (33) = 66\).
Time = 0.31 (sec) , antiderivative size = 383, normalized size of antiderivative = 10.64 \[ \int \left (-1+32 x-24 x^2+4 x^3+e^{2 x^2} \left (-8+66 x-32 x^2+4 x^3\right )+e^{x^2} \left (32-32 x+70 x^2-32 x^3+4 x^4\right )+e^{3 e^{2 x}-3 x} \left (e^{2 x^2} \left (24-48 e^{2 x}-32 x\right )-16 x+24 x^2-48 e^{2 x} x^2+e^{x^2} \left (-16+48 x-96 e^{2 x} x-32 x^2\right )\right )+e^{4 e^{2 x}-4 x} \left (2 x-4 x^2+8 e^{2 x} x^2+e^{2 x^2} \left (-4+8 e^{2 x}+4 x\right )+e^{x^2} \left (2-8 x+16 e^{2 x} x+4 x^2\right )\right )+e^{2 e^{2 x}-2 x} \left (48 x-54 x^2+4 x^3+e^{2 x^2} \left (-50+e^{2 x} (96-8 x)+100 x-8 x^2\right )+e^{2 x} \left (96 x^2-8 x^3\right )+e^{x^2} \left (48-104 x+104 x^2-8 x^3+e^{2 x} \left (192 x-16 x^2\right )\right )\right )+e^{e^{2 x}-x} \left (-64 x+56 x^2-8 x^3+e^{2 x} \left (-64 x^2+16 x^3\right )+e^{2 x^2} \left (40-136 x+32 x^2+e^{2 x} (-64+16 x)\right )+e^{x^2} \left (-64+96 x-144 x^2+32 x^3+e^{2 x} \left (-128 x+32 x^2\right )\right )\right )\right ) \, dx=x^{4} - 8 \, x^{3} + 16 \, x^{2} + {\left (x^{2} - 8 \, x + 16\right )} e^{\left (2 \, x^{2}\right )} + 2 \, {\left (x^{3} - 8 \, x^{2} + 16 \, x\right )} e^{\left (x^{2}\right )} - 8 \, {\left (x^{2} e^{\left (-2 \, x + 6 \, e^{\left (2 \, x\right )}\right )} + 2 \, x e^{\left (x^{2} - 2 \, x + 6 \, e^{\left (2 \, x\right )}\right )} + e^{\left (2 \, x^{2} - 2 \, x + 6 \, e^{\left (2 \, x\right )}\right )}\right )} e^{\left (-x - 3 \, e^{\left (2 \, x\right )}\right )} - 2 \, {\left (x^{3} e^{\left (4 \, e^{\left (2 \, x\right )}\right )} + 2 \, x^{2} e^{\left (x^{2} + 4 \, e^{\left (2 \, x\right )}\right )} - 12 \, x^{2} e^{\left (4 \, e^{\left (2 \, x\right )}\right )} + x e^{\left (2 \, x^{2} + 4 \, e^{\left (2 \, x\right )}\right )} - 24 \, x e^{\left (x^{2} + 4 \, e^{\left (2 \, x\right )}\right )} - 12 \, e^{\left (2 \, x^{2} + 4 \, e^{\left (2 \, x\right )}\right )}\right )} e^{\left (-2 \, x - 2 \, e^{\left (2 \, x\right )}\right )} + 8 \, {\left (x^{3} e^{\left (2 \, x + 2 \, e^{\left (2 \, x\right )}\right )} + 2 \, x^{2} e^{\left (x^{2} + 2 \, x + 2 \, e^{\left (2 \, x\right )}\right )} - 4 \, x^{2} e^{\left (2 \, x + 2 \, e^{\left (2 \, x\right )}\right )} + x e^{\left (2 \, x^{2} + 2 \, x + 2 \, e^{\left (2 \, x\right )}\right )} - 8 \, x e^{\left (x^{2} + 2 \, x + 2 \, e^{\left (2 \, x\right )}\right )} - 4 \, e^{\left (2 \, x^{2} + 2 \, x + 2 \, e^{\left (2 \, x\right )}\right )}\right )} e^{\left (-3 \, x - e^{\left (2 \, x\right )}\right )} + {\left (x^{2} e^{\left (-4 \, x + 8 \, e^{\left (2 \, x\right )}\right )} + 2 \, x e^{\left (x^{2} - 4 \, x + 8 \, e^{\left (2 \, x\right )}\right )} + e^{\left (2 \, x^{2} - 4 \, x + 8 \, e^{\left (2 \, x\right )}\right )}\right )} e^{\left (-4 \, e^{\left (2 \, x\right )}\right )} - x \]
integrate(((8*exp(x)^2+4*x-4)*exp(x^2)^2+(16*x*exp(x)^2+4*x^2-8*x+2)*exp(x ^2)+8*exp(x)^2*x^2-4*x^2+2*x)*exp(exp(x)^2-x)^4+((-48*exp(x)^2-32*x+24)*ex p(x^2)^2+(-96*x*exp(x)^2-32*x^2+48*x-16)*exp(x^2)-48*exp(x)^2*x^2+24*x^2-1 6*x)*exp(exp(x)^2-x)^3+(((-8*x+96)*exp(x)^2-8*x^2+100*x-50)*exp(x^2)^2+((- 16*x^2+192*x)*exp(x)^2-8*x^3+104*x^2-104*x+48)*exp(x^2)+(-8*x^3+96*x^2)*ex p(x)^2+4*x^3-54*x^2+48*x)*exp(exp(x)^2-x)^2+(((16*x-64)*exp(x)^2+32*x^2-13 6*x+40)*exp(x^2)^2+((32*x^2-128*x)*exp(x)^2+32*x^3-144*x^2+96*x-64)*exp(x^ 2)+(16*x^3-64*x^2)*exp(x)^2-8*x^3+56*x^2-64*x)*exp(exp(x)^2-x)+(4*x^3-32*x ^2+66*x-8)*exp(x^2)^2+(4*x^4-32*x^3+70*x^2-32*x+32)*exp(x^2)+4*x^3-24*x^2+ 32*x-1,x, algorithm=\
x^4 - 8*x^3 + 16*x^2 + (x^2 - 8*x + 16)*e^(2*x^2) + 2*(x^3 - 8*x^2 + 16*x) *e^(x^2) - 8*(x^2*e^(-2*x + 6*e^(2*x)) + 2*x*e^(x^2 - 2*x + 6*e^(2*x)) + e ^(2*x^2 - 2*x + 6*e^(2*x)))*e^(-x - 3*e^(2*x)) - 2*(x^3*e^(4*e^(2*x)) + 2* x^2*e^(x^2 + 4*e^(2*x)) - 12*x^2*e^(4*e^(2*x)) + x*e^(2*x^2 + 4*e^(2*x)) - 24*x*e^(x^2 + 4*e^(2*x)) - 12*e^(2*x^2 + 4*e^(2*x)))*e^(-2*x - 2*e^(2*x)) + 8*(x^3*e^(2*x + 2*e^(2*x)) + 2*x^2*e^(x^2 + 2*x + 2*e^(2*x)) - 4*x^2*e^ (2*x + 2*e^(2*x)) + x*e^(2*x^2 + 2*x + 2*e^(2*x)) - 8*x*e^(x^2 + 2*x + 2*e ^(2*x)) - 4*e^(2*x^2 + 2*x + 2*e^(2*x)))*e^(-3*x - e^(2*x)) + (x^2*e^(-4*x + 8*e^(2*x)) + 2*x*e^(x^2 - 4*x + 8*e^(2*x)) + e^(2*x^2 - 4*x + 8*e^(2*x) ))*e^(-4*e^(2*x)) - x
Time = 1.08 (sec) , antiderivative size = 225, normalized size of antiderivative = 6.25 \[ \int \left (-1+32 x-24 x^2+4 x^3+e^{2 x^2} \left (-8+66 x-32 x^2+4 x^3\right )+e^{x^2} \left (32-32 x+70 x^2-32 x^3+4 x^4\right )+e^{3 e^{2 x}-3 x} \left (e^{2 x^2} \left (24-48 e^{2 x}-32 x\right )-16 x+24 x^2-48 e^{2 x} x^2+e^{x^2} \left (-16+48 x-96 e^{2 x} x-32 x^2\right )\right )+e^{4 e^{2 x}-4 x} \left (2 x-4 x^2+8 e^{2 x} x^2+e^{2 x^2} \left (-4+8 e^{2 x}+4 x\right )+e^{x^2} \left (2-8 x+16 e^{2 x} x+4 x^2\right )\right )+e^{2 e^{2 x}-2 x} \left (48 x-54 x^2+4 x^3+e^{2 x^2} \left (-50+e^{2 x} (96-8 x)+100 x-8 x^2\right )+e^{2 x} \left (96 x^2-8 x^3\right )+e^{x^2} \left (48-104 x+104 x^2-8 x^3+e^{2 x} \left (192 x-16 x^2\right )\right )\right )+e^{e^{2 x}-x} \left (-64 x+56 x^2-8 x^3+e^{2 x} \left (-64 x^2+16 x^3\right )+e^{2 x^2} \left (40-136 x+32 x^2+e^{2 x} (-64+16 x)\right )+e^{x^2} \left (-64+96 x-144 x^2+32 x^3+e^{2 x} \left (-128 x+32 x^2\right )\right )\right )\right ) \, dx={\mathrm {e}}^{2\,x^2}\,\left (x^2-8\,x+16\right )-x-{\mathrm {e}}^{3\,{\mathrm {e}}^{2\,x}-3\,x}\,\left (8\,{\mathrm {e}}^{2\,x^2}+16\,x\,{\mathrm {e}}^{x^2}+8\,x^2\right )+{\mathrm {e}}^{x^2}\,\left (2\,x^3-16\,x^2+32\,x\right )+{\mathrm {e}}^{2\,{\mathrm {e}}^{2\,x}-2\,x}\,\left (24\,{\mathrm {e}}^{2\,x^2}+48\,x\,{\mathrm {e}}^{x^2}-2\,x\,{\mathrm {e}}^{2\,x^2}-4\,x^2\,{\mathrm {e}}^{x^2}+24\,x^2-2\,x^3\right )+{\mathrm {e}}^{4\,{\mathrm {e}}^{2\,x}-4\,x}\,\left ({\mathrm {e}}^{2\,x^2}+2\,x\,{\mathrm {e}}^{x^2}+x^2\right )+16\,x^2-8\,x^3+x^4-{\mathrm {e}}^{{\mathrm {e}}^{2\,x}-x}\,\left (32\,{\mathrm {e}}^{2\,x^2}+64\,x\,{\mathrm {e}}^{x^2}-8\,x\,{\mathrm {e}}^{2\,x^2}-16\,x^2\,{\mathrm {e}}^{x^2}+32\,x^2-8\,x^3\right ) \]
int(32*x + exp(2*exp(2*x) - 2*x)*(48*x - exp(2*x^2)*(exp(2*x)*(8*x - 96) - 100*x + 8*x^2 + 50) + exp(x^2)*(exp(2*x)*(192*x - 16*x^2) - 104*x + 104*x ^2 - 8*x^3 + 48) + exp(2*x)*(96*x^2 - 8*x^3) - 54*x^2 + 4*x^3) + exp(4*exp (2*x) - 4*x)*(2*x + exp(x^2)*(16*x*exp(2*x) - 8*x + 4*x^2 + 2) + 8*x^2*exp (2*x) + exp(2*x^2)*(4*x + 8*exp(2*x) - 4) - 4*x^2) - exp(3*exp(2*x) - 3*x) *(16*x + exp(x^2)*(96*x*exp(2*x) - 48*x + 32*x^2 + 16) + 48*x^2*exp(2*x) + exp(2*x^2)*(32*x + 48*exp(2*x) - 24) - 24*x^2) + exp(x^2)*(70*x^2 - 32*x - 32*x^3 + 4*x^4 + 32) + exp(2*x^2)*(66*x - 32*x^2 + 4*x^3 - 8) - exp(exp( 2*x) - x)*(64*x - exp(2*x^2)*(exp(2*x)*(16*x - 64) - 136*x + 32*x^2 + 40) + exp(x^2)*(exp(2*x)*(128*x - 32*x^2) - 96*x + 144*x^2 - 32*x^3 + 64) + ex p(2*x)*(64*x^2 - 16*x^3) - 56*x^2 + 8*x^3) - 24*x^2 + 4*x^3 - 1,x)
exp(2*x^2)*(x^2 - 8*x + 16) - x - exp(3*exp(2*x) - 3*x)*(8*exp(2*x^2) + 16 *x*exp(x^2) + 8*x^2) + exp(x^2)*(32*x - 16*x^2 + 2*x^3) + exp(2*exp(2*x) - 2*x)*(24*exp(2*x^2) + 48*x*exp(x^2) - 2*x*exp(2*x^2) - 4*x^2*exp(x^2) + 2 4*x^2 - 2*x^3) + exp(4*exp(2*x) - 4*x)*(exp(2*x^2) + 2*x*exp(x^2) + x^2) + 16*x^2 - 8*x^3 + x^4 - exp(exp(2*x) - x)*(32*exp(2*x^2) + 64*x*exp(x^2) - 8*x*exp(2*x^2) - 16*x^2*exp(x^2) + 32*x^2 - 8*x^3)