Q:

Calculate the integral $ \int_{0}^{1}(ax^2+bx+c)^{-3/{2}}dx $

How to calculate the integral below:
$$
\int_{0}^{1}(ax^2+bx+c)^{-3/{2}}dx
$$

A:

Hint:  Complete the square on $ax^2+bx+c$ and then try a trigonometric substitution.   Also, depending on the values of $a$, $b$, and $c$, the integral may be improper (and divergent).