# Integrate By Parts Or Use The Beta Function

Calculus Level 5

$I=\dfrac{\displaystyle \int_0^1 (1-x^{1729})^{1729} \, dx}{\displaystyle \int_0^1 (1-x^{1729})^{1728} \, dx}$

If $$I$$ can be represented as $$\frac{a}{b}$$, where $$a$$ and $$b$$ are coprime positive integers, find $$a+b$$.

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