Equation with integral

Question

I have the following equation:

$$\int (x-b)^n(x-c)^mdx = \frac{f(x)}{a}.$$

I want to compute value of $a$, but I don't know how can I escape this integral. $b$, $c$, $n$, $m$ are constants.

Answer 1

Well, you could derivate both sides and then solve for a - If $f'$ is not too complicated then you at least escape the integral.

$a = \frac{f'(x)} {(x-b)^n(x-c)^m} $