Integral of function involving powers of $x$

Question

What is the integral of following formula? If $a$ and $b$ are constant, and also $n$ and $m$ are cte.

$$\int (x-a)^n (b-x)^m dx$$

where $n, m, a,$ and $b$ are constants.

Answer 1

Just an idea: If n and m are integers: maybe you can use the binomial theorem?

Answer 2

Beside the formula given by Nasser, you can notice that the simple change of variable x = a + y makes the integrand simpler [replace (b -a) by c] . From here, as suggested by Bernd, using the binomial theorem, could be a rather simple solution. For sure, this assumes that "n" and "m" are integers.