\(\int (-1+32 x-24 x^2+4 x^3+e^{2 x^2} (-8+66 x-32 x^2+4 x^3)+e^{x^2} (32-32 x+70 x^2-32 x^3+4 x^4)+e^{3 e^{2 x}-3 x} (e^{2 x^2} (24-48 e^{2 x}-32 x)-16 x+24 x^2-48 e^{2 x} x^2+e^{x^2} (-16+48 x-96 e^{2 x} x-32 x^2))+e^{4 e^{2 x}-4 x} (2 x-4 x^2+8 e^{2 x} x^2+e^{2 x^2} (-4+8 e^{2 x}+4 x)+e^{x^2} (2-8 x+16 e^{2 x} x+4 x^2))+e^{2 e^{2 x}-2 x} (48 x-54 x^2+4 x^3+e^{2 x^2} (-50+e^{2 x} (96-8 x)+100 x-8 x^2)+e^{2 x} (96 x^2-8 x^3)+e^{x^2} (48-104 x+104 x^2-8 x^3+e^{2 x} (192 x-16 x^2)))+e^{e^{2 x}-x} (-64 x+56 x^2-8 x^3+e^{2 x} (-64 x^2+16 x^3)+e^{2 x^2} (40-136 x+32 x^2+e^{2 x} (-64+16 x))+e^{x^2} (-64+96 x-144 x^2+32 x^3+e^{2 x} (-128 x+32 x^2)))) \, dx\) [7443]

Optimal result

Integrand size = 436, antiderivative size = 36 \[ \int \left (-1+32 x-24 x^2+4 x^3+e^{2 x^2} \left (-8+66 x-32 x^2+4 x^3\right )+e^{x^2} \left (32-32 x+70 x^2-32 x^3+4 x^4\right )+e^{3 e^{2 x}-3 x} \left (e^{2 x^2} \left (24-48 e^{2 x}-32 x\right )-16 x+24 x^2-48 e^{2 x} x^2+e^{x^2} \left (-16+48 x-96 e^{2 x} x-32 x^2\right )\right )+e^{4 e^{2 x}-4 x} \left (2 x-4 x^2+8 e^{2 x} x^2+e^{2 x^2} \left (-4+8 e^{2 x}+4 x\right )+e^{x^2} \left (2-8 x+16 e^{2 x} x+4 x^2\right )\right )+e^{2 e^{2 x}-2 x} \left (48 x-54 x^2+4 x^3+e^{2 x^2} \left (-50+e^{2 x} (96-8 x)+100 x-8 x^2\right )+e^{2 x} \left (96 x^2-8 x^3\right )+e^{x^2} \left (48-104 x+104 x^2-8 x^3+e^{2 x} \left (192 x-16 x^2\right )\right )\right )+e^{e^{2 x}-x} \left (-64 x+56 x^2-8 x^3+e^{2 x} \left (-64 x^2+16 x^3\right )+e^{2 x^2} \left (40-136 x+32 x^2+e^{2 x} (-64+16 x)\right )+e^{x^2} \left (-64+96 x-144 x^2+32 x^3+e^{2 x} \left (-128 x+32 x^2\right )\right )\right )\right ) \, dx=-2-x+\left (e^{x^2}+x\right )^2 \left (-\left (-2+e^{e^{2 x}-x}\right )^2+x\right )^2 \]

[Out]

(x-(exp(exp(x)^2-x)-2)^2)^2*(exp(x^2)+x)^2-2-x

Rubi [F]

\[ \int \left (-1+32 x-24 x^2+4 x^3+e^{2 x^2} \left (-8+66 x-32 x^2+4 x^3\right )+e^{x^2} \left (32-32 x+70 x^2-32 x^3+4 x^4\right )+e^{3 e^{2 x}-3 x} \left (e^{2 x^2} \left (24-48 e^{2 x}-32 x\right )-16 x+24 x^2-48 e^{2 x} x^2+e^{x^2} \left (-16+48 x-96 e^{2 x} x-32 x^2\right )\right )+e^{4 e^{2 x}-4 x} \left (2 x-4 x^2+8 e^{2 x} x^2+e^{2 x^2} \left (-4+8 e^{2 x}+4 x\right )+e^{x^2} \left (2-8 x+16 e^{2 x} x+4 x^2\right )\right )+e^{2 e^{2 x}-2 x} \left (48 x-54 x^2+4 x^3+e^{2 x^2} \left (-50+e^{2 x} (96-8 x)+100 x-8 x^2\right )+e^{2 x} \left (96 x^2-8 x^3\right )+e^{x^2} \left (48-104 x+104 x^2-8 x^3+e^{2 x} \left (192 x-16 x^2\right )\right )\right )+e^{e^{2 x}-x} \left (-64 x+56 x^2-8 x^3+e^{2 x} \left (-64 x^2+16 x^3\right )+e^{2 x^2} \left (40-136 x+32 x^2+e^{2 x} (-64+16 x)\right )+e^{x^2} \left (-64+96 x-144 x^2+32 x^3+e^{2 x} \left (-128 x+32 x^2\right )\right )\right )\right ) \, dx=\int \left (-1+32 x-24 x^2+4 x^3+e^{2 x^2} \left (-8+66 x-32 x^2+4 x^3\right )+e^{x^2} \left (32-32 x+70 x^2-32 x^3+4 x^4\right )+e^{3 e^{2 x}-3 x} \left (e^{2 x^2} \left (24-48 e^{2 x}-32 x\right )-16 x+24 x^2-48 e^{2 x} x^2+e^{x^2} \left (-16+48 x-96 e^{2 x} x-32 x^2\right )\right )+e^{4 e^{2 x}-4 x} \left (2 x-4 x^2+8 e^{2 x} x^2+e^{2 x^2} \left (-4+8 e^{2 x}+4 x\right )+e^{x^2} \left (2-8 x+16 e^{2 x} x+4 x^2\right )\right )+e^{2 e^{2 x}-2 x} \left (48 x-54 x^2+4 x^3+e^{2 x^2} \left (-50+e^{2 x} (96-8 x)+100 x-8 x^2\right )+e^{2 x} \left (96 x^2-8 x^3\right )+e^{x^2} \left (48-104 x+104 x^2-8 x^3+e^{2 x} \left (192 x-16 x^2\right )\right )\right )+e^{e^{2 x}-x} \left (-64 x+56 x^2-8 x^3+e^{2 x} \left (-64 x^2+16 x^3\right )+e^{2 x^2} \left (40-136 x+32 x^2+e^{2 x} (-64+16 x)\right )+e^{x^2} \left (-64+96 x-144 x^2+32 x^3+e^{2 x} \left (-128 x+32 x^2\right )\right )\right )\right ) \, dx \]

[In]

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*(-1
6 + 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]

[Out]

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 - (8*E^(3*(E^(2*x) - x))*x*(x - 2*E^(2*x)*x))/(1 - 2*E^(2*x)) + (E^(4*(E^(2*x) - x))*x*(x - 2*E^(2*x)*x))/
(1 - 2*E^(2*x)) + 96*Defer[Int][E^(2*(E^(2*x) + x^2)), x] + 48*Defer[Int][E^(2*(E^(2*x) - x) + x^2), x] - 16*D
efer[Int][E^(3*(E^(2*x) - x) + x^2), x] + 2*Defer[Int][E^(4*(E^(2*x) - x) + x^2), x] - 4*Defer[Int][E^(2*(2*E^
(2*x) - 2*x + x^2)), x] - 64*Defer[Int][E^(E^(2*x) - x + x^2), x] - 50*Defer[Int][E^(2*(E^(2*x) - x + x^2)), x
] + 8*Defer[Int][E^(2*(2*E^(2*x) - x + x^2)), x] + 24*Defer[Int][E^(3*(E^(2*x) - x) + 2*x^2), x] + 40*Defer[In
t][E^(E^(2*x) - x + 2*x^2), x] - 64*Defer[Int][E^(E^(2*x) + x + 2*x^2), x] - 48*Defer[Int][E^(3*(E^(2*x) - x)
+ 2*x + 2*x^2), x] - 64*Defer[Int][E^(E^(2*x) - x)*x, x] + 48*Defer[Int][E^(2*(E^(2*x) - x))*x, x] - 8*Defer[I
nt][E^(2*(E^(2*x) + x^2))*x, x] + 192*Defer[Int][E^(2*E^(2*x) + x^2)*x, x] - 104*Defer[Int][E^(2*(E^(2*x) - x)
+ x^2)*x, x] + 48*Defer[Int][E^(3*(E^(2*x) - x) + x^2)*x, x] - 8*Defer[Int][E^(4*(E^(2*x) - x) + x^2)*x, x] +
4*Defer[Int][E^(2*(2*E^(2*x) - 2*x + x^2))*x, x] + 96*Defer[Int][E^(E^(2*x) - x + x^2)*x, x] + 100*Defer[Int]
[E^(2*(E^(2*x) - x + x^2))*x, x] - 128*Defer[Int][E^(E^(2*x) + x + x^2)*x, x] - 96*Defer[Int][E^(3*(E^(2*x) -
x) + 2*x + x^2)*x, x] + 16*Defer[Int][E^(4*(E^(2*x) - x) + 2*x + x^2)*x, x] - 32*Defer[Int][E^(3*(E^(2*x) - x)
+ 2*x^2)*x, x] - 136*Defer[Int][E^(E^(2*x) - x + 2*x^2)*x, x] + 16*Defer[Int][E^(E^(2*x) + x + 2*x^2)*x, x] +
96*Defer[Int][E^(2*E^(2*x))*x^2, x] + 56*Defer[Int][E^(E^(2*x) - x)*x^2, x] - 54*Defer[Int][E^(2*(E^(2*x) - x
))*x^2, x] - 64*Defer[Int][E^(E^(2*x) + x)*x^2, x] - 16*Defer[Int][E^(2*E^(2*x) + x^2)*x^2, x] + 104*Defer[Int
][E^(2*(E^(2*x) - x) + x^2)*x^2, x] - 32*Defer[Int][E^(3*(E^(2*x) - x) + x^2)*x^2, x] + 4*Defer[Int][E^(4*(E^(
2*x) - x) + x^2)*x^2, x] - 144*Defer[Int][E^(E^(2*x) - x + x^2)*x^2, x] - 8*Defer[Int][E^(2*(E^(2*x) - x + x^2
))*x^2, x] + 32*Defer[Int][E^(E^(2*x) + x + x^2)*x^2, x] + 32*Defer[Int][E^(E^(2*x) - x + 2*x^2)*x^2, x] - 8*D
efer[Int][E^(2*E^(2*x))*x^3, x] - 8*Defer[Int][E^(E^(2*x) - x)*x^3, x] + 4*Defer[Int][E^(2*(E^(2*x) - x))*x^3,
x] + 16*Defer[Int][E^(E^(2*x) + x)*x^3, x] - 8*Defer[Int][E^(2*(E^(2*x) - x) + x^2)*x^3, x] + 32*Defer[Int][E
^(E^(2*x) - x + x^2)*x^3, x]

Rubi steps \begin{align*} \text {integral}& = -x+16 x^2-8 x^3+x^4+\int e^{2 x^2} \left (-8+66 x-32 x^2+4 x^3\right ) \, dx+\int e^{x^2} \left (32-32 x+70 x^2-32 x^3+4 x^4\right ) \, dx+\int 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 ) \, dx+\int 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 ) \, dx+\int 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 ) \, dx+\int 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 ) \, dx \\ & = -x+16 x^2-8 x^3+x^4+\int 2 e^{4 \left (e^{2 x}-x\right )} \left (e^{x^2}+x\right ) \left (1+4 e^{x (2+x)}+2 e^{x^2} (-1+x)-2 x+4 e^{2 x} x\right ) \, dx+\int \left (-8 e^{2 x^2}+66 e^{2 x^2} x-32 e^{2 x^2} x^2+4 e^{2 x^2} x^3\right ) \, dx+\int \left (32 e^{x^2}-32 e^{x^2} x+70 e^{x^2} x^2-32 e^{x^2} x^3+4 e^{x^2} x^4\right ) \, dx+\int 8 e^{3 \left (e^{2 x}-x\right )} \left (e^{x^2}+x\right ) \left (-2-6 e^{x (2+x)}+3 x-6 e^{2 x} x-e^{x^2} (-3+4 x)\right ) \, dx+\int 2 e^{2 \left (e^{2 x}-x\right )} \left (e^{x^2}+x\right ) \left (24-4 e^{x (2+x)} (-12+x)-27 x-4 e^{2 x} (-12+x) x+2 x^2-e^{x^2} \left (25-50 x+4 x^2\right )\right ) \, dx+\int 8 e^{e^{2 x}-x} \left (e^{x^2}+x\right ) \left (-8+2 e^{x (2+x)} (-4+x)+7 x+2 e^{2 x} (-4+x) x-x^2+e^{x^2} \left (5-17 x+4 x^2\right )\right ) \, dx \\ & = -x+16 x^2-8 x^3+x^4+2 \int e^{4 \left (e^{2 x}-x\right )} \left (e^{x^2}+x\right ) \left (1+4 e^{x (2+x)}+2 e^{x^2} (-1+x)-2 x+4 e^{2 x} x\right ) \, dx+2 \int e^{2 \left (e^{2 x}-x\right )} \left (e^{x^2}+x\right ) \left (24-4 e^{x (2+x)} (-12+x)-27 x-4 e^{2 x} (-12+x) x+2 x^2-e^{x^2} \left (25-50 x+4 x^2\right )\right ) \, dx+4 \int e^{2 x^2} x^3 \, dx+4 \int e^{x^2} x^4 \, dx-8 \int e^{2 x^2} \, dx+8 \int e^{3 \left (e^{2 x}-x\right )} \left (e^{x^2}+x\right ) \left (-2-6 e^{x (2+x)}+3 x-6 e^{2 x} x-e^{x^2} (-3+4 x)\right ) \, dx+8 \int e^{e^{2 x}-x} \left (e^{x^2}+x\right ) \left (-8+2 e^{x (2+x)} (-4+x)+7 x+2 e^{2 x} (-4+x) x-x^2+e^{x^2} \left (5-17 x+4 x^2\right )\right ) \, dx+32 \int e^{x^2} \, dx-32 \int e^{x^2} x \, dx-32 \int e^{2 x^2} x^2 \, dx-32 \int e^{x^2} x^3 \, dx+66 \int e^{2 x^2} x \, dx+70 \int e^{x^2} x^2 \, dx \\ & = -16 e^{x^2}+\frac {33 e^{2 x^2}}{2}-x+35 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+16 \sqrt {\pi } \text {erfi}(x)-2 \sqrt {2 \pi } \text {erfi}\left (\sqrt {2} x\right )-2 \int e^{2 x^2} x \, dx+2 \int \left (4 e^{4 \left (e^{2 x}-x\right )+2 x+x^2} \left (e^{x^2}+x\right )+e^{4 \left (e^{2 x}-x\right )} \left (e^{x^2}+x\right ) \left (1-2 e^{x^2}-2 x+4 e^{2 x} x+2 e^{x^2} x\right )\right ) \, dx+2 \int \left (4 e^{2 \left (e^{2 x}-x\right )+2 x+x^2} (12-x) \left (e^{x^2}+x\right )-e^{2 \left (e^{2 x}-x\right )} \left (e^{x^2}+x\right ) \left (-24+25 e^{x^2}+27 x-48 e^{2 x} x-50 e^{x^2} x-2 x^2+4 e^{2 x} x^2+4 e^{x^2} x^2\right )\right ) \, dx-6 \int e^{x^2} x^2 \, dx+8 \int e^{2 x^2} \, dx+8 \int \left (6 e^{3 \left (e^{2 x}-x\right )+2 x+x^2} \left (-e^{x^2}-x\right )-e^{3 \left (e^{2 x}-x\right )} \left (e^{x^2}+x\right ) \left (2-3 e^{x^2}-3 x+6 e^{2 x} x+4 e^{x^2} x\right )\right ) \, dx+8 \int \left (2 e^{e^{2 x}+x+x^2} (4-x) \left (-e^{x^2}-x\right )+e^{e^{2 x}-x} \left (e^{x^2}+x\right ) \left (-8+5 e^{x^2}+7 x-8 e^{2 x} x-17 e^{x^2} x-x^2+2 e^{2 x} x^2+4 e^{x^2} x^2\right )\right ) \, dx+32 \int e^{x^2} x \, dx-35 \int e^{x^2} \, 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 {3}{2} \sqrt {\pi } \text {erfi}(x)+2 \int e^{4 \left (e^{2 x}-x\right )} \left (e^{x^2}+x\right ) \left (1-2 e^{x^2}-2 x+4 e^{2 x} x+2 e^{x^2} x\right ) \, dx-2 \int e^{2 \left (e^{2 x}-x\right )} \left (e^{x^2}+x\right ) \left (-24+25 e^{x^2}+27 x-48 e^{2 x} x-50 e^{x^2} x-2 x^2+4 e^{2 x} x^2+4 e^{x^2} x^2\right ) \, dx+3 \int e^{x^2} \, dx+8 \int e^{4 \left (e^{2 x}-x\right )+2 x+x^2} \left (e^{x^2}+x\right ) \, dx+8 \int e^{2 \left (e^{2 x}-x\right )+2 x+x^2} (12-x) \left (e^{x^2}+x\right ) \, dx-8 \int e^{3 \left (e^{2 x}-x\right )} \left (e^{x^2}+x\right ) \left (2-3 e^{x^2}-3 x+6 e^{2 x} x+4 e^{x^2} x\right ) \, dx+8 \int e^{e^{2 x}-x} \left (e^{x^2}+x\right ) \left (-8+5 e^{x^2}+7 x-8 e^{2 x} x-17 e^{x^2} x-x^2+2 e^{2 x} x^2+4 e^{x^2} x^2\right ) \, dx+16 \int e^{e^{2 x}+x+x^2} (4-x) \left (-e^{x^2}-x\right ) \, dx+48 \int e^{3 \left (e^{2 x}-x\right )+2 x+x^2} \left (-e^{x^2}-x\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+2 \int \left (2 e^{4 \left (e^{2 x}-x\right )+2 x^2} (-1+x)+e^{4 \left (e^{2 x}-x\right )} x \left (1-2 x+4 e^{2 x} x\right )+e^{4 \left (e^{2 x}-x\right )+x^2} \left (1-4 x+4 e^{2 x} x+2 x^2\right )\right ) \, dx-2 \int e^{2 \left (e^{2 x}-x\right )} \left (e^{x^2}+x\right ) \left (-24+27 x+4 e^{2 x} (-12+x) x-2 x^2+e^{x^2} \left (25-50 x+4 x^2\right )\right ) \, dx+8 \int e^{2 e^{2 x}+x^2} (12-x) \left (e^{x^2}+x\right ) \, dx+8 \int \left (e^{4 \left (e^{2 x}-x\right )+2 x+2 x^2}+e^{4 \left (e^{2 x}-x\right )+2 x+x^2} x\right ) \, dx-8 \int \left (e^{3 \left (e^{2 x}-x\right )+2 x^2} (-3+4 x)+e^{3 \left (e^{2 x}-x\right )} x \left (2-3 x+6 e^{2 x} x\right )+2 e^{3 \left (e^{2 x}-x\right )+x^2} \left (1-3 x+3 e^{2 x} x+2 x^2\right )\right ) \, dx+8 \int e^{e^{2 x}-x} \left (e^{x^2}+x\right ) \left (-8+7 x+2 e^{2 x} (-4+x) x-x^2+e^{x^2} \left (5-17 x+4 x^2\right )\right ) \, dx+16 \int \left (e^{e^{2 x}+x+2 x^2} (-4+x)+e^{e^{2 x}+x+x^2} (-4+x) x\right ) \, dx+48 \int \left (-e^{3 \left (e^{2 x}-x\right )+2 x+2 x^2}-e^{3 \left (e^{2 x}-x\right )+2 x+x^2} x\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+2 \int e^{4 \left (e^{2 x}-x\right )} x \left (1-2 x+4 e^{2 x} x\right ) \, dx+2 \int e^{4 \left (e^{2 x}-x\right )+x^2} \left (1-4 x+4 e^{2 x} x+2 x^2\right ) \, dx-2 \int \left (e^{2 \left (e^{2 x}-x\right )+2 x^2} \left (25-50 x+4 x^2\right )+e^{2 \left (e^{2 x}-x\right )} x \left (-24+27 x-48 e^{2 x} x-2 x^2+4 e^{2 x} x^2\right )+4 e^{2 \left (e^{2 x}-x\right )+x^2} \left (-6+13 x-12 e^{2 x} x-13 x^2+e^{2 x} x^2+x^3\right )\right ) \, dx+4 \int e^{4 \left (e^{2 x}-x\right )+2 x^2} (-1+x) \, dx+8 \int e^{4 \left (e^{2 x}-x\right )+2 x+2 x^2} \, dx+8 \int e^{4 \left (e^{2 x}-x\right )+2 x+x^2} x \, dx-8 \int e^{3 \left (e^{2 x}-x\right )+2 x^2} (-3+4 x) \, dx-8 \int e^{3 \left (e^{2 x}-x\right )} x \left (2-3 x+6 e^{2 x} x\right ) \, dx+8 \int \left (-e^{2 e^{2 x}+2 x^2} (-12+x)-e^{2 e^{2 x}+x^2} (-12+x) x\right ) \, dx+8 \int \left (e^{e^{2 x}-x+2 x^2} \left (5-17 x+4 x^2\right )+e^{e^{2 x}-x} x \left (-8+7 x-8 e^{2 x} x-x^2+2 e^{2 x} x^2\right )+2 e^{e^{2 x}-x+x^2} \left (-4+6 x-4 e^{2 x} x-9 x^2+e^{2 x} x^2+2 x^3\right )\right ) \, dx+16 \int e^{e^{2 x}+x+2 x^2} (-4+x) \, dx+16 \int e^{e^{2 x}+x+x^2} (-4+x) x \, dx-16 \int e^{3 \left (e^{2 x}-x\right )+x^2} \left (1-3 x+3 e^{2 x} x+2 x^2\right ) \, dx-48 \int e^{3 \left (e^{2 x}-x\right )+2 x+2 x^2} \, dx-48 \int e^{3 \left (e^{2 x}-x\right )+2 x+x^2} x \, 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 {8 e^{3 \left (e^{2 x}-x\right )} x \left (x-2 e^{2 x} x\right )}{1-2 e^{2 x}}+\frac {e^{4 \left (e^{2 x}-x\right )} x \left (x-2 e^{2 x} x\right )}{1-2 e^{2 x}}-2 \int e^{2 \left (e^{2 x}-x\right )+2 x^2} \left (25-50 x+4 x^2\right ) \, dx-2 \int e^{2 \left (e^{2 x}-x\right )} x \left (-24+27 x-48 e^{2 x} x-2 x^2+4 e^{2 x} x^2\right ) \, dx+2 \int \left (e^{4 \left (e^{2 x}-x\right )+x^2}-4 e^{4 \left (e^{2 x}-x\right )+x^2} x+4 e^{4 \left (e^{2 x}-x\right )+2 x+x^2} x+2 e^{4 \left (e^{2 x}-x\right )+x^2} x^2\right ) \, dx+4 \int e^{2 \left (2 e^{2 x}-2 x+x^2\right )} (-1+x) \, dx+8 \int e^{2 \left (2 e^{2 x}-x+x^2\right )} \, dx-8 \int e^{2 e^{2 x}+2 x^2} (-12+x) \, dx+8 \int e^{4 \left (e^{2 x}-x\right )+2 x+x^2} x \, dx-8 \int e^{2 e^{2 x}+x^2} (-12+x) x \, dx-8 \int \left (-3 e^{3 \left (e^{2 x}-x\right )+2 x^2}+4 e^{3 \left (e^{2 x}-x\right )+2 x^2} x\right ) \, dx+8 \int e^{e^{2 x}-x+2 x^2} \left (5-17 x+4 x^2\right ) \, dx+8 \int e^{e^{2 x}-x} x \left (-8+7 x-8 e^{2 x} x-x^2+2 e^{2 x} x^2\right ) \, dx-8 \int e^{2 \left (e^{2 x}-x\right )+x^2} \left (-6+13 x-12 e^{2 x} x-13 x^2+e^{2 x} x^2+x^3\right ) \, dx+16 \int \left (-4 e^{e^{2 x}+x+2 x^2}+e^{e^{2 x}+x+2 x^2} x\right ) \, dx-16 \int \left (e^{3 \left (e^{2 x}-x\right )+x^2}-3 e^{3 \left (e^{2 x}-x\right )+x^2} x+3 e^{3 \left (e^{2 x}-x\right )+2 x+x^2} x+2 e^{3 \left (e^{2 x}-x\right )+x^2} x^2\right ) \, dx+16 \int \left (-4 e^{e^{2 x}+x+x^2} x+e^{e^{2 x}+x+x^2} x^2\right ) \, dx+16 \int e^{e^{2 x}-x+x^2} \left (-4+6 x-4 e^{2 x} x-9 x^2+e^{2 x} x^2+2 x^3\right ) \, dx-48 \int e^{3 \left (e^{2 x}-x\right )+2 x+2 x^2} \, dx-48 \int e^{3 \left (e^{2 x}-x\right )+2 x+x^2} x \, 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 {8 e^{3 \left (e^{2 x}-x\right )} x \left (x-2 e^{2 x} x\right )}{1-2 e^{2 x}}+\frac {e^{4 \left (e^{2 x}-x\right )} x \left (x-2 e^{2 x} x\right )}{1-2 e^{2 x}}+2 \int e^{4 \left (e^{2 x}-x\right )+x^2} \, dx-2 \int e^{2 \left (e^{2 x}-x+x^2\right )} \left (25-50 x+4 x^2\right ) \, dx-2 \int \left (4 e^{2 \left (e^{2 x}-x\right )+2 x} (-12+x) x^2-e^{2 \left (e^{2 x}-x\right )} x \left (24-27 x+2 x^2\right )\right ) \, dx+4 \int e^{4 \left (e^{2 x}-x\right )+x^2} x^2 \, dx+4 \int \left (-e^{2 \left (2 e^{2 x}-2 x+x^2\right )}+e^{2 \left (2 e^{2 x}-2 x+x^2\right )} x\right ) \, dx+8 \int e^{2 \left (2 e^{2 x}-x+x^2\right )} \, dx-8 \int e^{2 \left (e^{2 x}+x^2\right )} (-12+x) \, dx-8 \int e^{4 \left (e^{2 x}-x\right )+x^2} x \, dx+2 \left (8 \int e^{4 \left (e^{2 x}-x\right )+2 x+x^2} x \, dx\right )-8 \int \left (-12 e^{2 e^{2 x}+x^2} x+e^{2 e^{2 x}+x^2} x^2\right ) \, dx+8 \int \left (5 e^{e^{2 x}-x+2 x^2}-17 e^{e^{2 x}-x+2 x^2} x+4 e^{e^{2 x}-x+2 x^2} x^2\right ) \, dx-8 \int \left (-6 e^{2 \left (e^{2 x}-x\right )+x^2}+13 e^{2 \left (e^{2 x}-x\right )+x^2} x-12 e^{2 \left (e^{2 x}-x\right )+2 x+x^2} x-13 e^{2 \left (e^{2 x}-x\right )+x^2} x^2+e^{2 \left (e^{2 x}-x\right )+2 x+x^2} x^2+e^{2 \left (e^{2 x}-x\right )+x^2} x^3\right ) \, dx+8 \int \left (2 e^{e^{2 x}+x} (-4+x) x^2-e^{e^{2 x}-x} x \left (8-7 x+x^2\right )\right ) \, dx-16 \int e^{3 \left (e^{2 x}-x\right )+x^2} \, dx+16 \int e^{e^{2 x}+x+2 x^2} x \, dx+16 \int e^{e^{2 x}+x+x^2} x^2 \, dx+16 \int \left (-4 e^{e^{2 x}-x+x^2}+6 e^{e^{2 x}-x+x^2} x-4 e^{e^{2 x}+x+x^2} x-9 e^{e^{2 x}-x+x^2} x^2+e^{e^{2 x}+x+x^2} x^2+2 e^{e^{2 x}-x+x^2} x^3\right ) \, dx+24 \int e^{3 \left (e^{2 x}-x\right )+2 x^2} \, dx-32 \int e^{3 \left (e^{2 x}-x\right )+2 x^2} x \, dx-32 \int e^{3 \left (e^{2 x}-x\right )+x^2} x^2 \, dx-48 \int e^{3 \left (e^{2 x}-x\right )+2 x+2 x^2} \, dx+48 \int e^{3 \left (e^{2 x}-x\right )+x^2} x \, dx-2 \left (48 \int e^{3 \left (e^{2 x}-x\right )+2 x+x^2} x \, dx\right )-64 \int e^{e^{2 x}+x+2 x^2} \, dx-64 \int e^{e^{2 x}+x+x^2} x \, 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 {8 e^{3 \left (e^{2 x}-x\right )} x \left (x-2 e^{2 x} x\right )}{1-2 e^{2 x}}+\frac {e^{4 \left (e^{2 x}-x\right )} x \left (x-2 e^{2 x} x\right )}{1-2 e^{2 x}}+2 \int e^{4 \left (e^{2 x}-x\right )+x^2} \, dx+2 \int e^{2 \left (e^{2 x}-x\right )} x \left (24-27 x+2 x^2\right ) \, dx-2 \int \left (25 e^{2 \left (e^{2 x}-x+x^2\right )}-50 e^{2 \left (e^{2 x}-x+x^2\right )} x+4 e^{2 \left (e^{2 x}-x+x^2\right )} x^2\right ) \, dx-4 \int e^{2 \left (2 e^{2 x}-2 x+x^2\right )} \, dx+4 \int e^{2 \left (2 e^{2 x}-2 x+x^2\right )} x \, dx+4 \int e^{4 \left (e^{2 x}-x\right )+x^2} x^2 \, dx+8 \int e^{2 \left (2 e^{2 x}-x+x^2\right )} \, dx-8 \int e^{4 \left (e^{2 x}-x\right )+x^2} x \, dx+2 \left (8 \int e^{4 \left (e^{2 x}-x\right )+2 x+x^2} x \, dx\right )-8 \int e^{2 e^{2 x}+x^2} x^2 \, dx-8 \int e^{2 \left (e^{2 x}-x\right )+2 x+x^2} x^2 \, dx-8 \int e^{2 \left (e^{2 x}-x\right )+2 x} (-12+x) x^2 \, dx-8 \int e^{2 \left (e^{2 x}-x\right )+x^2} x^3 \, dx-8 \int \left (-12 e^{2 \left (e^{2 x}+x^2\right )}+e^{2 \left (e^{2 x}+x^2\right )} x\right ) \, dx-8 \int e^{e^{2 x}-x} x \left (8-7 x+x^2\right ) \, dx-16 \int e^{3 \left (e^{2 x}-x\right )+x^2} \, dx+16 \int e^{e^{2 x}+x+2 x^2} x \, dx+2 \left (16 \int e^{e^{2 x}+x+x^2} x^2 \, dx\right )+16 \int e^{e^{2 x}+x} (-4+x) x^2 \, dx+24 \int e^{3 \left (e^{2 x}-x\right )+2 x^2} \, dx-32 \int e^{3 \left (e^{2 x}-x\right )+2 x^2} x \, dx-32 \int e^{3 \left (e^{2 x}-x\right )+x^2} x^2 \, dx+32 \int e^{e^{2 x}-x+2 x^2} x^2 \, dx+32 \int e^{e^{2 x}-x+x^2} x^3 \, dx+40 \int e^{e^{2 x}-x+2 x^2} \, dx+48 \int e^{2 \left (e^{2 x}-x\right )+x^2} \, dx-48 \int e^{3 \left (e^{2 x}-x\right )+2 x+2 x^2} \, dx+48 \int e^{3 \left (e^{2 x}-x\right )+x^2} x \, dx-2 \left (48 \int e^{3 \left (e^{2 x}-x\right )+2 x+x^2} x \, dx\right )-64 \int e^{e^{2 x}-x+x^2} \, dx-64 \int e^{e^{2 x}+x+2 x^2} \, dx-2 \left (64 \int e^{e^{2 x}+x+x^2} x \, dx\right )+96 \int e^{2 e^{2 x}+x^2} x \, dx+96 \int e^{e^{2 x}-x+x^2} x \, dx+96 \int e^{2 \left (e^{2 x}-x\right )+2 x+x^2} x \, dx-104 \int e^{2 \left (e^{2 x}-x\right )+x^2} x \, dx+104 \int e^{2 \left (e^{2 x}-x\right )+x^2} x^2 \, dx-136 \int e^{e^{2 x}-x+2 x^2} x \, dx-144 \int e^{e^{2 x}-x+x^2} x^2 \, 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 {8 e^{3 \left (e^{2 x}-x\right )} x \left (x-2 e^{2 x} x\right )}{1-2 e^{2 x}}+\frac {e^{4 \left (e^{2 x}-x\right )} x \left (x-2 e^{2 x} x\right )}{1-2 e^{2 x}}+2 \int e^{4 \left (e^{2 x}-x\right )+x^2} \, dx+2 \int \left (24 e^{2 \left (e^{2 x}-x\right )} x-27 e^{2 \left (e^{2 x}-x\right )} x^2+2 e^{2 \left (e^{2 x}-x\right )} x^3\right ) \, dx-4 \int e^{2 \left (2 e^{2 x}-2 x+x^2\right )} \, dx+4 \int e^{2 \left (2 e^{2 x}-2 x+x^2\right )} x \, dx+4 \int e^{4 \left (e^{2 x}-x\right )+x^2} x^2 \, dx+8 \int e^{2 \left (2 e^{2 x}-x+x^2\right )} \, dx-8 \int e^{2 \left (e^{2 x}+x^2\right )} x \, dx-8 \int e^{4 \left (e^{2 x}-x\right )+x^2} x \, dx+2 \left (8 \int e^{4 \left (e^{2 x}-x\right )+2 x+x^2} x \, dx\right )-2 \left (8 \int e^{2 e^{2 x}+x^2} x^2 \, dx\right )-8 \int e^{2 \left (e^{2 x}-x+x^2\right )} x^2 \, dx-8 \int e^{2 e^{2 x}} (-12+x) x^2 \, dx-8 \int e^{2 \left (e^{2 x}-x\right )+x^2} x^3 \, dx-8 \int \left (8 e^{e^{2 x}-x} x-7 e^{e^{2 x}-x} x^2+e^{e^{2 x}-x} x^3\right ) \, dx-16 \int e^{3 \left (e^{2 x}-x\right )+x^2} \, dx+16 \int e^{e^{2 x}+x+2 x^2} x \, dx+2 \left (16 \int e^{e^{2 x}+x+x^2} x^2 \, dx\right )+16 \int \left (-4 e^{e^{2 x}+x} x^2+e^{e^{2 x}+x} x^3\right ) \, dx+24 \int e^{3 \left (e^{2 x}-x\right )+2 x^2} \, dx-32 \int e^{3 \left (e^{2 x}-x\right )+2 x^2} x \, dx-32 \int e^{3 \left (e^{2 x}-x\right )+x^2} x^2 \, dx+32 \int e^{e^{2 x}-x+2 x^2} x^2 \, dx+32 \int e^{e^{2 x}-x+x^2} x^3 \, dx+40 \int e^{e^{2 x}-x+2 x^2} \, dx+48 \int e^{2 \left (e^{2 x}-x\right )+x^2} \, dx-48 \int e^{3 \left (e^{2 x}-x\right )+2 x+2 x^2} \, dx+48 \int e^{3 \left (e^{2 x}-x\right )+x^2} x \, dx-2 \left (48 \int e^{3 \left (e^{2 x}-x\right )+2 x+x^2} x \, dx\right )-50 \int e^{2 \left (e^{2 x}-x+x^2\right )} \, dx-64 \int e^{e^{2 x}-x+x^2} \, dx-64 \int e^{e^{2 x}+x+2 x^2} \, dx-2 \left (64 \int e^{e^{2 x}+x+x^2} x \, dx\right )+96 \int e^{2 \left (e^{2 x}+x^2\right )} \, dx+2 \left (96 \int e^{2 e^{2 x}+x^2} x \, dx\right )+96 \int e^{e^{2 x}-x+x^2} x \, dx+100 \int e^{2 \left (e^{2 x}-x+x^2\right )} x \, dx-104 \int e^{2 \left (e^{2 x}-x\right )+x^2} x \, dx+104 \int e^{2 \left (e^{2 x}-x\right )+x^2} x^2 \, dx-136 \int e^{e^{2 x}-x+2 x^2} x \, dx-144 \int e^{e^{2 x}-x+x^2} x^2 \, 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 {8 e^{3 \left (e^{2 x}-x\right )} x \left (x-2 e^{2 x} x\right )}{1-2 e^{2 x}}+\frac {e^{4 \left (e^{2 x}-x\right )} x \left (x-2 e^{2 x} x\right )}{1-2 e^{2 x}}+2 \int e^{4 \left (e^{2 x}-x\right )+x^2} \, dx-4 \int e^{2 \left (2 e^{2 x}-2 x+x^2\right )} \, dx+4 \int e^{2 \left (2 e^{2 x}-2 x+x^2\right )} x \, dx+4 \int e^{4 \left (e^{2 x}-x\right )+x^2} x^2 \, dx+4 \int e^{2 \left (e^{2 x}-x\right )} x^3 \, dx+8 \int e^{2 \left (2 e^{2 x}-x+x^2\right )} \, dx-8 \int e^{2 \left (e^{2 x}+x^2\right )} x \, dx-8 \int e^{4 \left (e^{2 x}-x\right )+x^2} x \, dx+2 \left (8 \int e^{4 \left (e^{2 x}-x\right )+2 x+x^2} x \, dx\right )-2 \left (8 \int e^{2 e^{2 x}+x^2} x^2 \, dx\right )-8 \int e^{2 \left (e^{2 x}-x+x^2\right )} x^2 \, dx-8 \int e^{e^{2 x}-x} x^3 \, dx-8 \int e^{2 \left (e^{2 x}-x\right )+x^2} x^3 \, dx-8 \int \left (-12 e^{2 e^{2 x}} x^2+e^{2 e^{2 x}} x^3\right ) \, dx-16 \int e^{3 \left (e^{2 x}-x\right )+x^2} \, dx+16 \int e^{e^{2 x}+x+2 x^2} x \, dx+2 \left (16 \int e^{e^{2 x}+x+x^2} x^2 \, dx\right )+16 \int e^{e^{2 x}+x} x^3 \, dx+24 \int e^{3 \left (e^{2 x}-x\right )+2 x^2} \, dx-32 \int e^{3 \left (e^{2 x}-x\right )+2 x^2} x \, dx-32 \int e^{3 \left (e^{2 x}-x\right )+x^2} x^2 \, dx+32 \int e^{e^{2 x}-x+2 x^2} x^2 \, dx+32 \int e^{e^{2 x}-x+x^2} x^3 \, dx+40 \int e^{e^{2 x}-x+2 x^2} \, dx+48 \int e^{2 \left (e^{2 x}-x\right )+x^2} \, dx-48 \int e^{3 \left (e^{2 x}-x\right )+2 x+2 x^2} \, dx+48 \int e^{2 \left (e^{2 x}-x\right )} x \, dx+48 \int e^{3 \left (e^{2 x}-x\right )+x^2} x \, dx-2 \left (48 \int e^{3 \left (e^{2 x}-x\right )+2 x+x^2} x \, dx\right )-50 \int e^{2 \left (e^{2 x}-x+x^2\right )} \, dx-54 \int e^{2 \left (e^{2 x}-x\right )} x^2 \, dx+56 \int e^{e^{2 x}-x} x^2 \, dx-64 \int e^{e^{2 x}-x+x^2} \, dx-64 \int e^{e^{2 x}+x+2 x^2} \, dx-64 \int e^{e^{2 x}-x} x \, dx-2 \left (64 \int e^{e^{2 x}+x+x^2} x \, dx\right )-64 \int e^{e^{2 x}+x} x^2 \, dx+96 \int e^{2 \left (e^{2 x}+x^2\right )} \, dx+2 \left (96 \int e^{2 e^{2 x}+x^2} x \, dx\right )+96 \int e^{e^{2 x}-x+x^2} x \, dx+100 \int e^{2 \left (e^{2 x}-x+x^2\right )} x \, dx-104 \int e^{2 \left (e^{2 x}-x\right )+x^2} x \, dx+104 \int e^{2 \left (e^{2 x}-x\right )+x^2} x^2 \, dx-136 \int e^{e^{2 x}-x+2 x^2} x \, dx-144 \int e^{e^{2 x}-x+x^2} x^2 \, 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 {8 e^{3 \left (e^{2 x}-x\right )} x \left (x-2 e^{2 x} x\right )}{1-2 e^{2 x}}+\frac {e^{4 \left (e^{2 x}-x\right )} x \left (x-2 e^{2 x} x\right )}{1-2 e^{2 x}}+2 \int e^{4 \left (e^{2 x}-x\right )+x^2} \, dx-4 \int e^{2 \left (2 e^{2 x}-2 x+x^2\right )} \, dx+4 \int e^{2 \left (2 e^{2 x}-2 x+x^2\right )} x \, dx+4 \int e^{4 \left (e^{2 x}-x\right )+x^2} x^2 \, dx+4 \int e^{2 \left (e^{2 x}-x\right )} x^3 \, dx+8 \int e^{2 \left (2 e^{2 x}-x+x^2\right )} \, dx-8 \int e^{2 \left (e^{2 x}+x^2\right )} x \, dx-8 \int e^{4 \left (e^{2 x}-x\right )+x^2} x \, dx+2 \left (8 \int e^{4 \left (e^{2 x}-x\right )+2 x+x^2} x \, dx\right )-2 \left (8 \int e^{2 e^{2 x}+x^2} x^2 \, dx\right )-8 \int e^{2 \left (e^{2 x}-x+x^2\right )} x^2 \, dx-8 \int e^{2 e^{2 x}} x^3 \, dx-8 \int e^{e^{2 x}-x} x^3 \, dx-8 \int e^{2 \left (e^{2 x}-x\right )+x^2} x^3 \, dx-16 \int e^{3 \left (e^{2 x}-x\right )+x^2} \, dx+16 \int e^{e^{2 x}+x+2 x^2} x \, dx+2 \left (16 \int e^{e^{2 x}+x+x^2} x^2 \, dx\right )+16 \int e^{e^{2 x}+x} x^3 \, dx+24 \int e^{3 \left (e^{2 x}-x\right )+2 x^2} \, dx-32 \int e^{3 \left (e^{2 x}-x\right )+2 x^2} x \, dx-32 \int e^{3 \left (e^{2 x}-x\right )+x^2} x^2 \, dx+32 \int e^{e^{2 x}-x+2 x^2} x^2 \, dx+32 \int e^{e^{2 x}-x+x^2} x^3 \, dx+40 \int e^{e^{2 x}-x+2 x^2} \, dx+48 \int e^{2 \left (e^{2 x}-x\right )+x^2} \, dx-48 \int e^{3 \left (e^{2 x}-x\right )+2 x+2 x^2} \, dx+48 \int e^{2 \left (e^{2 x}-x\right )} x \, dx+48 \int e^{3 \left (e^{2 x}-x\right )+x^2} x \, dx-2 \left (48 \int e^{3 \left (e^{2 x}-x\right )+2 x+x^2} x \, dx\right )-50 \int e^{2 \left (e^{2 x}-x+x^2\right )} \, dx-54 \int e^{2 \left (e^{2 x}-x\right )} x^2 \, dx+56 \int e^{e^{2 x}-x} x^2 \, dx-64 \int e^{e^{2 x}-x+x^2} \, dx-64 \int e^{e^{2 x}+x+2 x^2} \, dx-64 \int e^{e^{2 x}-x} x \, dx-2 \left (64 \int e^{e^{2 x}+x+x^2} x \, dx\right )-64 \int e^{e^{2 x}+x} x^2 \, dx+96 \int e^{2 \left (e^{2 x}+x^2\right )} \, dx+2 \left (96 \int e^{2 e^{2 x}+x^2} x \, dx\right )+96 \int e^{e^{2 x}-x+x^2} x \, dx+96 \int e^{2 e^{2 x}} x^2 \, dx+100 \int e^{2 \left (e^{2 x}-x+x^2\right )} x \, dx-104 \int e^{2 \left (e^{2 x}-x\right )+x^2} x \, dx+104 \int e^{2 \left (e^{2 x}-x\right )+x^2} x^2 \, dx-136 \int e^{e^{2 x}-x+2 x^2} x \, dx-144 \int e^{e^{2 x}-x+x^2} x^2 \, dx \\ \end{align*}

Mathematica [B] (verified)

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 \[ \int \left (-1+32 x-24 x^2+4 x^3+e^{2 x^2} \left (-8+66 x-32 x^2+4 x^3\right )+e^{x^2} \left (32-32 x+70 x^2-32 x^3+4 x^4\right )+e^{3 e^{2 x}-3 x} \left (e^{2 x^2} \left (24-48 e^{2 x}-32 x\right )-16 x+24 x^2-48 e^{2 x} x^2+e^{x^2} \left (-16+48 x-96 e^{2 x} x-32 x^2\right )\right )+e^{4 e^{2 x}-4 x} \left (2 x-4 x^2+8 e^{2 x} x^2+e^{2 x^2} \left (-4+8 e^{2 x}+4 x\right )+e^{x^2} \left (2-8 x+16 e^{2 x} x+4 x^2\right )\right )+e^{2 e^{2 x}-2 x} \left (48 x-54 x^2+4 x^3+e^{2 x^2} \left (-50+e^{2 x} (96-8 x)+100 x-8 x^2\right )+e^{2 x} \left (96 x^2-8 x^3\right )+e^{x^2} \left (48-104 x+104 x^2-8 x^3+e^{2 x} \left (192 x-16 x^2\right )\right )\right )+e^{e^{2 x}-x} \left (-64 x+56 x^2-8 x^3+e^{2 x} \left (-64 x^2+16 x^3\right )+e^{2 x^2} \left (40-136 x+32 x^2+e^{2 x} (-64+16 x)\right )+e^{x^2} \left (-64+96 x-144 x^2+32 x^3+e^{2 x} \left (-128 x+32 x^2\right )\right )\right )\right ) \, dx=16 e^{2 x^2}-x+32 e^{x^2} x-8 e^{2 x^2} x+16 x^2-16 e^{x^2} x^2+e^{2 x^2} x^2-8 x^3+2 e^{x^2} x^3+x^4+\frac {2 e^{4 e^{2 x}-4 x} \left (e^{x^2}+x\right ) \left (-2 e^{x^2}+4 e^{2 x+x^2}-2 x+4 e^{2 x} x\right )}{-4+8 e^{2 x}}-\frac {8 e^{3 e^{2 x}-3 x} \left (e^{x^2}+x\right ) \left (-3 e^{x^2}+6 e^{2 x+x^2}-3 x+6 e^{2 x} x\right )}{-3+6 e^{2 x}}-2 e^{2 e^{2 x}} \left (e^{-2 x+2 x^2} (-12+x)+e^{-2 x+x^2} \left (-24 x+2 x^2\right )+e^{-2 x} \left (-12 x^2+x^3\right )\right )+8 e^{e^{2 x}} \left (e^{-x+2 x^2} (-4+x)+e^{-x+x^2} \left (-8 x+2 x^2\right )+e^{-x} \left (-4 x^2+x^3\right )\right ) \]

[In]

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]

[Out]

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)

Maple [B] (verified)

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	\(-x +{\mathrm e}^{2 x^{2}} x^{2}+2 x^{3} {\mathrm e}^{x^{2}}-8 x \,{\mathrm e}^{2 x^{2}}+32 \,{\mathrm e}^{x^{2}} x +16 \,{\mathrm e}^{2 x^{2}}+x^{4}-8 x^{3}+16 x^{2}-16 x^{2} {\mathrm e}^{x^{2}}+2 \,{\mathrm e}^{x^{2}} {\mathrm e}^{4 \,{\mathrm e}^{2 x}-4 x} x -16 \,{\mathrm e}^{x^{2}} {\mathrm e}^{3 \,{\mathrm e}^{2 x}-3 x} x +48 \,{\mathrm e}^{x^{2}} {\mathrm e}^{2 \,{\mathrm e}^{2 x}-2 x} x -64 \,{\mathrm e}^{x^{2}} {\mathrm e}^{{\mathrm e}^{2 x}-x} x -2 \,{\mathrm e}^{2 x^{2}} {\mathrm e}^{2 \,{\mathrm e}^{2 x}-2 x} x +8 \,{\mathrm e}^{2 x^{2}} {\mathrm e}^{{\mathrm e}^{2 x}-x} x -4 \,{\mathrm e}^{x^{2}} {\mathrm e}^{2 \,{\mathrm e}^{2 x}-2 x} x^{2}+16 \,{\mathrm e}^{x^{2}} {\mathrm e}^{{\mathrm e}^{2 x}-x} x^{2}-2 \,{\mathrm e}^{2 \,{\mathrm e}^{2 x}-2 x} x^{3}+8 \,{\mathrm e}^{{\mathrm e}^{2 x}-x} x^{3}+{\mathrm e}^{4 \,{\mathrm e}^{2 x}-4 x} x^{2}-8 \,{\mathrm e}^{3 \,{\mathrm e}^{2 x}-3 x} x^{2}+24 \,{\mathrm e}^{2 \,{\mathrm e}^{2 x}-2 x} x^{2}-32 \,{\mathrm e}^{{\mathrm e}^{2 x}-x} x^{2}+{\mathrm e}^{2 x^{2}} {\mathrm e}^{4 \,{\mathrm e}^{2 x}-4 x}-8 \,{\mathrm e}^{2 x^{2}} {\mathrm e}^{3 \,{\mathrm e}^{2 x}-3 x}+24 \,{\mathrm e}^{2 x^{2}} {\mathrm e}^{2 \,{\mathrm e}^{2 x}-2 x}-32 \,{\mathrm e}^{2 x^{2}} {\mathrm e}^{{\mathrm e}^{2 x}-x}\)	\(380\)

[In]

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)
*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)*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)

[Out]

(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

Fricas [B] (verification not implemented)

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 \[ \int \left (-1+32 x-24 x^2+4 x^3+e^{2 x^2} \left (-8+66 x-32 x^2+4 x^3\right )+e^{x^2} \left (32-32 x+70 x^2-32 x^3+4 x^4\right )+e^{3 e^{2 x}-3 x} \left (e^{2 x^2} \left (24-48 e^{2 x}-32 x\right )-16 x+24 x^2-48 e^{2 x} x^2+e^{x^2} \left (-16+48 x-96 e^{2 x} x-32 x^2\right )\right )+e^{4 e^{2 x}-4 x} \left (2 x-4 x^2+8 e^{2 x} x^2+e^{2 x^2} \left (-4+8 e^{2 x}+4 x\right )+e^{x^2} \left (2-8 x+16 e^{2 x} x+4 x^2\right )\right )+e^{2 e^{2 x}-2 x} \left (48 x-54 x^2+4 x^3+e^{2 x^2} \left (-50+e^{2 x} (96-8 x)+100 x-8 x^2\right )+e^{2 x} \left (96 x^2-8 x^3\right )+e^{x^2} \left (48-104 x+104 x^2-8 x^3+e^{2 x} \left (192 x-16 x^2\right )\right )\right )+e^{e^{2 x}-x} \left (-64 x+56 x^2-8 x^3+e^{2 x} \left (-64 x^2+16 x^3\right )+e^{2 x^2} \left (40-136 x+32 x^2+e^{2 x} (-64+16 x)\right )+e^{x^2} \left (-64+96 x-144 x^2+32 x^3+e^{2 x} \left (-128 x+32 x^2\right )\right )\right )\right ) \, dx=x^{4} - 8 \, x^{3} + 16 \, x^{2} + {\left (x^{2} - 8 \, x + 16\right )} e^{\left (2 \, x^{2}\right )} + 2 \, {\left (x^{3} - 8 \, x^{2} + 16 \, x\right )} e^{\left (x^{2}\right )} + 8 \, {\left (x^{3} - 4 \, x^{2} + {\left (x - 4\right )} e^{\left (2 \, x^{2}\right )} + 2 \, {\left (x^{2} - 4 \, x\right )} e^{\left (x^{2}\right )}\right )} e^{\left (-x + e^{\left (2 \, x\right )}\right )} - 2 \, {\left (x^{3} - 12 \, x^{2} + {\left (x - 12\right )} e^{\left (2 \, x^{2}\right )} + 2 \, {\left (x^{2} - 12 \, x\right )} e^{\left (x^{2}\right )}\right )} e^{\left (-2 \, x + 2 \, e^{\left (2 \, x\right )}\right )} - 8 \, {\left (x^{2} + 2 \, x e^{\left (x^{2}\right )} + e^{\left (2 \, x^{2}\right )}\right )} e^{\left (-3 \, x + 3 \, e^{\left (2 \, x\right )}\right )} + {\left (x^{2} + 2 \, x e^{\left (x^{2}\right )} + e^{\left (2 \, x^{2}\right )}\right )} e^{\left (-4 \, x + 4 \, e^{\left (2 \, x\right )}\right )} - x \]

[In]

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(ex
p(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+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^3-2
4*x^2+32*x-1,x, algorithm="fricas")

[Out]

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

Sympy [B] (verification not implemented)

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 \[ \int \left (-1+32 x-24 x^2+4 x^3+e^{2 x^2} \left (-8+66 x-32 x^2+4 x^3\right )+e^{x^2} \left (32-32 x+70 x^2-32 x^3+4 x^4\right )+e^{3 e^{2 x}-3 x} \left (e^{2 x^2} \left (24-48 e^{2 x}-32 x\right )-16 x+24 x^2-48 e^{2 x} x^2+e^{x^2} \left (-16+48 x-96 e^{2 x} x-32 x^2\right )\right )+e^{4 e^{2 x}-4 x} \left (2 x-4 x^2+8 e^{2 x} x^2+e^{2 x^2} \left (-4+8 e^{2 x}+4 x\right )+e^{x^2} \left (2-8 x+16 e^{2 x} x+4 x^2\right )\right )+e^{2 e^{2 x}-2 x} \left (48 x-54 x^2+4 x^3+e^{2 x^2} \left (-50+e^{2 x} (96-8 x)+100 x-8 x^2\right )+e^{2 x} \left (96 x^2-8 x^3\right )+e^{x^2} \left (48-104 x+104 x^2-8 x^3+e^{2 x} \left (192 x-16 x^2\right )\right )\right )+e^{e^{2 x}-x} \left (-64 x+56 x^2-8 x^3+e^{2 x} \left (-64 x^2+16 x^3\right )+e^{2 x^2} \left (40-136 x+32 x^2+e^{2 x} (-64+16 x)\right )+e^{x^2} \left (-64+96 x-144 x^2+32 x^3+e^{2 x} \left (-128 x+32 x^2\right )\right )\right )\right ) \, dx=x^{4} - 8 x^{3} + 16 x^{2} - x + \left (- 8 x^{2} - 16 x e^{x^{2}} - 8 e^{2 x^{2}}\right ) e^{- 3 x + 3 e^{2 x}} + \left (x^{2} - 8 x + 16\right ) e^{2 x^{2}} + \left (x^{2} + 2 x e^{x^{2}} + e^{2 x^{2}}\right ) e^{- 4 x + 4 e^{2 x}} + \left (2 x^{3} - 16 x^{2} + 32 x\right ) e^{x^{2}} + \left (- 2 x^{3} - 4 x^{2} e^{x^{2}} + 24 x^{2} - 2 x e^{2 x^{2}} + 48 x e^{x^{2}} + 24 e^{2 x^{2}}\right ) e^{- 2 x + 2 e^{2 x}} + \left (8 x^{3} + 16 x^{2} e^{x^{2}} - 32 x^{2} + 8 x e^{2 x^{2}} - 64 x e^{x^{2}} - 32 e^{2 x^{2}}\right ) e^{- x + e^{2 x}} \]

[In]

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*ex
p(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+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+9
6*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)*ex
p(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)

[Out]

x**4 - 8*x**3 + 16*x**2 - x + (-8*x**2 - 16*x*exp(x**2) - 8*exp(2*x**2))*exp(-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)*ex
p(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))

Maxima [B] (verification not implemented)

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 \[ \int \left (-1+32 x-24 x^2+4 x^3+e^{2 x^2} \left (-8+66 x-32 x^2+4 x^3\right )+e^{x^2} \left (32-32 x+70 x^2-32 x^3+4 x^4\right )+e^{3 e^{2 x}-3 x} \left (e^{2 x^2} \left (24-48 e^{2 x}-32 x\right )-16 x+24 x^2-48 e^{2 x} x^2+e^{x^2} \left (-16+48 x-96 e^{2 x} x-32 x^2\right )\right )+e^{4 e^{2 x}-4 x} \left (2 x-4 x^2+8 e^{2 x} x^2+e^{2 x^2} \left (-4+8 e^{2 x}+4 x\right )+e^{x^2} \left (2-8 x+16 e^{2 x} x+4 x^2\right )\right )+e^{2 e^{2 x}-2 x} \left (48 x-54 x^2+4 x^3+e^{2 x^2} \left (-50+e^{2 x} (96-8 x)+100 x-8 x^2\right )+e^{2 x} \left (96 x^2-8 x^3\right )+e^{x^2} \left (48-104 x+104 x^2-8 x^3+e^{2 x} \left (192 x-16 x^2\right )\right )\right )+e^{e^{2 x}-x} \left (-64 x+56 x^2-8 x^3+e^{2 x} \left (-64 x^2+16 x^3\right )+e^{2 x^2} \left (40-136 x+32 x^2+e^{2 x} (-64+16 x)\right )+e^{x^2} \left (-64+96 x-144 x^2+32 x^3+e^{2 x} \left (-128 x+32 x^2\right )\right )\right )\right ) \, dx=x^{4} - 8 \, x^{3} + 16 \, x^{2} + {\left (x^{2} - 8 \, x + 16\right )} e^{\left (2 \, x^{2}\right )} + 2 \, {\left (x^{3} - 8 \, x^{2} + 16 \, x\right )} e^{\left (x^{2}\right )} + 8 \, {\left (x^{3} - 4 \, x^{2} + {\left (x - 4\right )} e^{\left (2 \, x^{2}\right )} + 2 \, {\left (x^{2} - 4 \, x\right )} e^{\left (x^{2}\right )}\right )} e^{\left (-x + e^{\left (2 \, x\right )}\right )} - 2 \, {\left (x^{3} - 12 \, x^{2} + {\left (x - 12\right )} e^{\left (2 \, x^{2}\right )} + 2 \, {\left (x^{2} - 12 \, x\right )} e^{\left (x^{2}\right )}\right )} e^{\left (-2 \, x + 2 \, e^{\left (2 \, x\right )}\right )} - 8 \, {\left (x^{2} + 2 \, x e^{\left (x^{2}\right )} + e^{\left (2 \, x^{2}\right )}\right )} e^{\left (-3 \, x + 3 \, e^{\left (2 \, x\right )}\right )} + {\left (x^{2} + 2 \, x e^{\left (x^{2}\right )} + e^{\left (2 \, x^{2}\right )}\right )} e^{\left (-4 \, x + 4 \, e^{\left (2 \, x\right )}\right )} - x \]

[In]

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(ex
p(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+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^3-2
4*x^2+32*x-1,x, algorithm="maxima")

[Out]

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

Giac [B] (verification not implemented)

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 \]

[In]

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(ex
p(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+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^3-2
4*x^2+32*x-1,x, algorithm="giac")

[Out]

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

Mupad [B] (verification not implemented)

Time = 1.08 (sec) , antiderivative size = 225, normalized size of antiderivative = 6.25 \[ \int \left (-1+32 x-24 x^2+4 x^3+e^{2 x^2} \left (-8+66 x-32 x^2+4 x^3\right )+e^{x^2} \left (32-32 x+70 x^2-32 x^3+4 x^4\right )+e^{3 e^{2 x}-3 x} \left (e^{2 x^2} \left (24-48 e^{2 x}-32 x\right )-16 x+24 x^2-48 e^{2 x} x^2+e^{x^2} \left (-16+48 x-96 e^{2 x} x-32 x^2\right )\right )+e^{4 e^{2 x}-4 x} \left (2 x-4 x^2+8 e^{2 x} x^2+e^{2 x^2} \left (-4+8 e^{2 x}+4 x\right )+e^{x^2} \left (2-8 x+16 e^{2 x} x+4 x^2\right )\right )+e^{2 e^{2 x}-2 x} \left (48 x-54 x^2+4 x^3+e^{2 x^2} \left (-50+e^{2 x} (96-8 x)+100 x-8 x^2\right )+e^{2 x} \left (96 x^2-8 x^3\right )+e^{x^2} \left (48-104 x+104 x^2-8 x^3+e^{2 x} \left (192 x-16 x^2\right )\right )\right )+e^{e^{2 x}-x} \left (-64 x+56 x^2-8 x^3+e^{2 x} \left (-64 x^2+16 x^3\right )+e^{2 x^2} \left (40-136 x+32 x^2+e^{2 x} (-64+16 x)\right )+e^{x^2} \left (-64+96 x-144 x^2+32 x^3+e^{2 x} \left (-128 x+32 x^2\right )\right )\right )\right ) \, dx={\mathrm {e}}^{2\,x^2}\,\left (x^2-8\,x+16\right )-x-{\mathrm {e}}^{3\,{\mathrm {e}}^{2\,x}-3\,x}\,\left (8\,{\mathrm {e}}^{2\,x^2}+16\,x\,{\mathrm {e}}^{x^2}+8\,x^2\right )+{\mathrm {e}}^{x^2}\,\left (2\,x^3-16\,x^2+32\,x\right )+{\mathrm {e}}^{2\,{\mathrm {e}}^{2\,x}-2\,x}\,\left (24\,{\mathrm {e}}^{2\,x^2}+48\,x\,{\mathrm {e}}^{x^2}-2\,x\,{\mathrm {e}}^{2\,x^2}-4\,x^2\,{\mathrm {e}}^{x^2}+24\,x^2-2\,x^3\right )+{\mathrm {e}}^{4\,{\mathrm {e}}^{2\,x}-4\,x}\,\left ({\mathrm {e}}^{2\,x^2}+2\,x\,{\mathrm {e}}^{x^2}+x^2\right )+16\,x^2-8\,x^3+x^4-{\mathrm {e}}^{{\mathrm {e}}^{2\,x}-x}\,\left (32\,{\mathrm {e}}^{2\,x^2}+64\,x\,{\mathrm {e}}^{x^2}-8\,x\,{\mathrm {e}}^{2\,x^2}-16\,x^2\,{\mathrm {e}}^{x^2}+32\,x^2-8\,x^3\right ) \]

[In]

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*e
xp(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) + exp(2*x)*(64*x^2 - 16*x^3) - 56*
x^2 + 8*x^3) - 24*x^2 + 4*x^3 - 1,x)

[Out]

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) +
24*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)