Question

How can you integrate `xe^(x^2) dx` using integration by parts?

Answer 1

We do not need to integrate by parts, but since that is what is specified:

We can integrate `xe^(x^2)dx` by sustitution `w=x^2` and we end up with

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

Therefore, to use parts, I will choose `u=1` and `dv=xe^(x^2)dx`

This makes `du=0dx` and `v= 1/2 e^(x^2)`

The parts formula gives us;

`1/2e^(x^2)- int 0 dx`

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