Integration of xe^x^2

`intx(e^(x^2))dx`

Let's apply integral substitution,

Substitute `u=x^2`

`(du)/dx=2x`

`=>du=2xdx`

`=>dx=(1/(2x))du`

`intxe^(x^2)dx=intxe^u(1/(2x))du`

`=int1/2e^udu`

`=1/2inte^udu`

`=1/2e^u`

Substitute back `u=x^2`

`=1/2e^(x^2)`

Add a constant C to the solution,

`=1/2e^(x^2)+C`