Question

integrate e^2x with respect to x

Answer 1

[integral] x e^2x dx

I choose
u = x
du = dx
v = e^2x
dv = e^2x dx

Using Integration by parts
[integral] x e^2x = x e^2x - [integral] e^2x dx

the last integral is certainly easier than the one I started out with so I know things are good.

So I integrate [integral] e^2x dx to become e^2x + C. Plugging this in my whole answer is

[integral] x e^2x = x e^2x - e^2x + C