let $I =\int \frac{1}{3+2 \sin x+\cos x} d x$put $\tan \left(\frac{x}{2}\right)=t$$\begin{aligned} & x=2 \tan ^{-1} t \\ & d x=\frac{2 d t}{1+t^2} \text { and } \sin x=2 \frac{t}{1+t^2}, \cos x\left(\frac{1-t^2}{1+t^2}\right)\end{aligned}$
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$\sin (\log x)$