# What is the antiderivative of #1/(2+sinx)#?

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The antiderivative of ( \frac{1}{2+\sin(x)} ) is ( -\frac{2}{\sqrt{3}}\tan^{-1}\left(\frac{\tan\left(\frac{x}{2}\right)+\sqrt{3}}{\sqrt{3}-\tan\left(\frac{x}{2}\right)}\right)+C ), where ( C ) is the constant of integration.

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