1.

  \[\int \frac{2\sin x}{(3+sin2x)}dx\]is equal to

A. \[\frac{1}{2}\ln \left| \frac{2+\sin x-\cos x}{2-\sin x+\cos x} \right|-\frac{1}{\sqrt{2}}{{\tan }^{-1}}\left( \frac{\sin x+\cos x}{\sqrt{2}} \right)+c\]
B. \[\frac{1}{2}\ln \left| \frac{2+\sin x-\cos x}{2-\sin x+\cos x} \right|-\frac{1}{2\sqrt{2}}{{\tan }^{-1}}\left( \frac{\sin x+\cos x}{\sqrt{2}} \right)+c\]
C. \[\frac{1}{4}\ln \left| \frac{2+\sin x-\cos x}{2-\sin x+\cos x} \right|-\frac{1}{\sqrt{2}}{{\tan }^{-1}}\left( \frac{\sin x+\cos x}{\sqrt{2}} \right)+c\]
D. none of these
Answer» D. none of these


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