How to solve for dx in the numerator by itself

Question

$$\int \frac{dx}{1+x^2} $$ I'm having a hard time knowing what to do when it's just dx on top

Answer 1

If this was your confusion: the integral is precisely by definition equal to $$\int \frac{1}{1+x^2} \ \mathrm{d}x$$ which is a very well-known integral.

Answer 2

$$\int \frac{1}{1+x^2} \space dx = \tan^{-1}(x) + C$$