Struggling with integration in a Differential Equations problem

Question

This is part of a hw problem for school. (the original problem is the DE $x' = x^2 -4$) It is a differential equations course but I'm stuck on a calculus part. I plugged the integral to wolfram alpha and can't follow why the integral of $\displaystyle \int \dfrac{1}{1-u^2} du = \dfrac{1}{2} \left(\log(u+1)-\log(1-u)\right)+ C$

Answer 1

Hint: $\dfrac{1}{1-u^2}=\dfrac{A}{1-u}+\dfrac{B}{1+u}$, for some $A,B\in \Bbb R$. Find $A$ and $B$.