Calculate $\int_0^{2\pi} \frac{1}{2+\sin(x)} \ dx$

Yes, absolutely correct but you may try alternative approach by converting $\sin\space x$ into $\tan\space (x/2)$ $$\sin(x) = \frac{2\cdot \tan(x/2)}{1+\tan^2(x/2)}$$.

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Integration

Analysis

Real Analysis

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