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Help needed - Mathematica code


I would greatly appreciate if anyone can help me out of this problem.

To explain my problem, I will use LaTeX code.

Given a>0, 1>b>0, c>0 and d>0, I want to calculate the following

\int_0^a X Y(X)^b dX

where Y(X) is defined by

(c - \frac{Y}{d-X Y^b}) X Y^{b-1}=1

Can you tell me Mathematica codes for this problem?

Thank you in advance.


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