This one is a really tough one for me. I'm betting an integration via partial fractions : $\displaystyle \int \frac{2a^2x-6a+1}{a^2x^2-6ax+10}dx$ with $\displaystyle a \neq 0$.

I could reach that the integral is worth $\displaystyle \int 1+\frac{-a^2x^2+6ax-9+2a^2x-6a}{a^2x^2-6ax+10}dx$. I don't know how to proceed from it. A first attempt would be to factorize that denominator, but it's not an easy task for me!