Let $P(x) = a_nx^n + ..... a_1x + a_0$
Is there a general technique for integrating
$$\frac{P(x)}{\sqrt{Ax^2 + Bx + C}}$$
Similarly is there a general method for
$$\frac{1}{P(x)\sqrt{Ax^2 + Bx + C}}$$
And finally is there a general method for
$$\frac{P(x)}{Q(x)\sqrt{Ax^2 + Bx + C}}$$
Where Q(x) is similarly defined to P(x).