# Using All The Basic Techniques of Integration

Calculus Level 5

$\large \int_{0}^{\pi} \frac{\sin x(\sin x + 1)e^{\sin x + \cos x}}{e^{\cos x}+1} dx = a + b\int_{0}^{\pi}e^{\sin x} dx$

Given the equation above, where $$a$$ and $$b$$ are positive rational numbers, find the value of $$100(a^2+b^2).$$

Note: $$\displaystyle \int_{0}^{\pi}e^{\sin x} dx$$ is irrational.

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