How to solve this integral: $\int \frac{\sqrt{-x^2 - x + 2}}{x^2}dx$?

Question

Question is self explanatory. I have an exam and our professor gave us questions. This is the one I couldn't do. Any ideas would be very helpful:

$$\int \frac{\sqrt{-x^2 - x + 2}}{x^2}dx$$

Answer 1

Hint: set $$\sqrt{-x^2-x+2}=xt+\sqrt{2}$$ we get $$x=\frac{-2t\sqrt{2}-1}{t^2+1}$$ and $$dx=\frac{2(-\sqrt{2}+t+\sqrt{2}t^2)}{(1+t^2)^2}dt$$