How to integrate $\int \frac{f'(x)}{f^2(x)}$? In my book it states $\int \frac{f^1(x)}{f^2(x)}=-\frac{1}{f(x)}$.
I don't really understand why and it doesn't say in my book.
My first idea was maybe we can cancle out $f^1(x)$. So  $\int \frac{f^1(x)}{f^2(x)} = \int \frac{1}{f^1(x)}$.
But I'm not sure if you can do that and it also doesn't explain the minus from $-\frac{1}{f(x)}$ .

$\displaystyle \int \frac{f'(x) } {(f(x) )^2 }dx =- \frac{1}{f(x)} + c$,  so is it possible your expression represents that? 
