# The integration ratio

Calculus Level 5

$\large{I_{n}=\displaystyle \int^{\pi}_{0} e^{x}(\sin x)^{n} \, dx}$

Define $$I_n$$ as the integral above. If $$\large{\dfrac{I_{5}}{I_{1}}=\dfrac{a}{b}}$$ where $$a,b$$ are coprime integers, find $$a+b$$.

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