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I'm wondering which substitution I need to transform the integral:

$$ \int_0^2 x^a (2-x)^b dx $$

so that the endpoints will become $0$ and $1$ , and the second argument of the form $(1-x)^c$ in order to solve it by using the beta function.

Gennaro Arguzzi
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    You should use $x=2y$. You'll find $c=b$. – J.G. Feb 13 '22 at 17:18
  • Hello @J.G. thank you very much for your precious suggestion. Can you take a look to this question please? https://math.stackexchange.com/questions/4381786/solving-int-02-zn-a-2-2-z-1b-dz-by-using-beta-function – Gennaro Arguzzi Feb 14 '22 at 09:46
  • I've looked. Unfortunately, until @peek-a-boo's latest comment is addressed, there's nothing more to say. – J.G. Feb 14 '22 at 11:24

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