How do you integrate (x^3)(e^x^2) ?

x^3 * e^(x^2) * dx
x^2 * e^(x^2) * x * dx

u = x^2
du = 2x * dx
(1/2) * du = x * dx

u * e^(u) * (1/2) * du

(1/2) * u * e^(u) * dx

a = u
da = du
db = e^(u) * du
b = e^(u)

(1/2) * (u * e^(u) - int(e^(u) * du)) =>
(1/2) * (u * e^(u) - e^(u)) + C =>
(1/2) * (u - 1) * e^(u) + C =>
(1/2) * (x^2 - 1) * e^(x^2) + C

w = x² leads to [ 1 / 2 ] w e^w dw which is an integration by parts...u = w , dv = e^w dw