We have to determine `int x*e^(x^2) dx`

Let `y = x^2` , `dy/dx = 2x` => x*dx = (1/2)*dy

=> `int e^y*(1/2) dy`

=> `e^y/2 + C`

Substitute y = x^2

=> `e^(x^2)/2 + C`

**The required integral is** `e^(x^2)/2 + C`

We have to determine `int x*e^(x^2) dx`

Let `y = x^2` , `dy/dx = 2x` => x*dx = (1/2)*dy

=> `int e^y*(1/2) dy`

=> `e^y/2 + C`

Substitute y = x^2

=> `e^(x^2)/2 + C`

**The required integral is** `e^(x^2)/2 + C`