Question

How do you integrate `xe^(x^2) dx`?

Answer 1

This can be done by substitution. See explanation.

Explanation:

`intxe^(x^2)dx=|(t=x^2),(dt=2xdx),(dt/2=xdx)|=int(e^t/2)dt=1/2int(e^tdt)`

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