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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.

Michael Albanese
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vdrake6
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    What about $f$? – agha Jul 20 '14 at 22:07
  • I don't know specific representation of f function. It's possible to compute this at all? – vdrake6 Jul 20 '14 at 22:14
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    Something about $f$ should be given, for example that it is a monic polynomial. Otherwise, we can multiply both $f$ and $a$ by an arbitrary constant ($\neq 0$) and the value of $a$ cannot be determined. – Ragnar Jul 20 '14 at 22:15
  • I am sure that f is a real polynomial, but I'm not sure that f is monic polynomial. – vdrake6 Jul 20 '14 at 22:20
  • Then its as simple as this: its not possible to compute what $a$ is. If you say $f$ is monic then its simple: $a = n+m+1$ (consider the largest power of $x$ on the l.h.s.) – Winther Jul 20 '14 at 22:22

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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} $