Integration conundrum

No.9369800 ViewReplyOriginalReport
Undergrad baby here learning baby match plz no bully.
Im taking math 2 next trimester so I will be learning integration.
I decided I didnt want to wait a month to learn how to integrate so I took it upon myself to teach myself to integrate and everything has gone fine and dandy except for one issue I have with reversing the chain rule.

Lets say you have something like:

[e^(x^2)]2x its anti derivative clearly is e^(x^2), given that d/dx[e^(x^2)] = {d/dx[e^(x^2)]}{d/dx(x^2)}

But what if you have something like e^(x^2) by itself? No function I know differentiates into something like that.