Write a value


Write a value of $\int \frac{\cos \mathrm{x}}{3+2 \sin \mathrm{x}} \mathrm{dx}$.


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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