As the title suggests, I want to evaluate: $\int \frac{dx}{(ax^2 + bx + c)\sqrt{px +q}}$ given $a,p \neq 0$.
I tried the substitution $px + q = t^2$, which yields: $ \int \frac{dt}{(At^4 + Bt^2 + C)}$ where $A,B,C$ are some constants such that $A \neq 0$. How do I solve this new integral, or is there an easier substitution?
($A = \frac{a}{p^2} $, $B = \frac{bp - 2aq}{p^2} $ and $C = \frac{aq^2 - bpq + cp^2}{p^2} $)