Question:
Write a value of $\int \frac{\cos \mathrm{x}}{3+2 \sin \mathrm{x}} \mathrm{dx}$.
Solution:
let $3+2 \sin x=t$
Differentiating on both sides we get,
$2 \cos x d x=d t$
$\cos x d x=\frac{1}{2} d t$
Substituting above equation in $\int \frac{\cos x}{3+2 \sin x} d x$ we get,
$\int \frac{1}{2 t} d t$
$=\frac{1}{2} \log t+c$
$=\frac{1}{2} \log (3+2 \sin x)+c$
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