how do i find this integral?

Question

xe^(x^2)*dx

Answer 1

I = ∫ x e ^( x ² ) dx
Let u = x ²
du = 2 x dx
du / 2 = x dx
I = (1 / 2) ∫ e^u du
I = (1 / 2) e^u + C
I = (1 / 2) e^( x ² ) + C

Answer 2

∫xe^(x²)dx

put x² = t

differentiating with respect to x,
2xdx = dt

thus,
½∫e^t dt = ½ e^t
= ½ e^(x²) (re-substituting value of x²)
is the solution.