\( \int \frac{2 \sin x}{(3+\sin 2 x)} d x \) is equal to \( \mathrm...

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\( \int \frac{2 \sin x}{(3+\sin 2 x)} d x \) is equal to
\( \mathrm{P} \)
(1) \( \frac{1}{2} \ln \left|\frac{2+\sin x-\cos x}{2-\sin x+\cos x}\right|-\frac{1}{\sqrt{2}} \tan ^{-1}\left(\frac{\sin x+\cos x}{\sqrt{2}}\right)+c \)
W
(2) \( \frac{1}{2} \ln \left|\frac{2+\sin x-\cos x}{2-\sin x+\cos x}\right|-\frac{1}{2 \sqrt{2}} \tan ^{-1}\left(\frac{\sin x+\cos x}{\sqrt{2}}\right)+c \)
(3) \( \frac{1}{4} \ln \left|\frac{2+\sin x-\cos x}{2-\sin x+\cos x}\right|-\frac{1}{\sqrt{2}} \tan ^{-1}\left(\frac{\sin x+\cos x}{\sqrt{2}}\right)+c \)
(4) none of these
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