Question

How to find the antiderivative of `(5x)/(x^2-1)dx`?

Answer 1

The answer is: `y'=ln|x^2-1|+c`.

Since

`int(f'(x))/f(x)dx=ln|f(x)|+c`,

than:

`int(5x)/(x^2-1)dx=5/2int(2x)/(x^2-1)dx=ln|x^2-1|+c`.