Calculus 8 : Rational t'gos

Calculus Level 3

\[ \large \int_{0}^{\pi} \dfrac{1}{1+\sin x} \, dx \]

If the value of above integral is of the form \(\large a^b\), where \(a\) and \(b\) are coprime integers, find the value of \(\dfrac{a}{b}\).

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