Put and the integral you'll get is a basic one, it comes from the derivative of secant.
No, you have to substitute back. And the 2 is in the denominator !
Because when subbing y=x², dy=2x dx ---> dx=dy/(2x)
a way to check a result : Wolfram Mathematica Online Integrator
Here is what I would do :
Substituting ? Not good. The dy will have a nasty expression !
Substituting ? Not bad... But it would be something weird though
Another method ? Why not ?
Now, substitue
Going back to the integral :
Do you see any simplification with the red parts ??
Edit : you could have substituted , but it doesn't matter, you got it