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

Question

8506 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-05-19T19:34:08

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;

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

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

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