## Calculus (3rd Edition)

$\frac{1}{2}\ln|2\sin x+3|+C$
We have $$\int \frac{\cos x}{2\sin x+3}dx =\frac{1}{2} \int \frac{2\cos x}{2\sin x+3}dx\\ =\frac{1}{2}\ln|2\sin x+3|+c.$$ where we used the facts that $(\sin u)'=\cos u$ and $\int \frac{u'}{u}=\ln u$.