integrating help, using a u substitution of differential equation

Question

$ dy = \frac{1}{1+x^{2}} dx $

How would I integrate this ? Can I use a u substitution?

let $ u = 1+x^{2} dx $

$ du = 2x dx $

am not sure how to go from here?

Any help appreciated thanks

Answer 1

The integral of $\frac{1}{1+x^2}$ is equal to $\tan^{-1}(x)$, so you can evaluate your expression to give $y = \tan^{-1}(x) + c$

Answer 2

The solution is $y=\arctan x+c$ using the standard integral