Integration with reciprocal

Question

$$\int\frac1{y-y^2}\,dy$$ Not sure how to do.

I tried substitution, not sure if product rule would work?

Answer 1

Hint

Can you find $a$ and $b$ so that $$\frac1{y-y^2}=\frac1{y(1-y)}=\frac ay+\frac b{y-1}\ ?$$

Answer 2

Try completing the square. $$\frac{1}{y-y^2} = \frac{1}{-\left(y-\frac{1}{2}\right)^2+\frac{1}{4}}$$

Now substitute $u = y-\frac{1}{2}$.