∫sin x ( 3+2cos x #160; ) dx ∫( 3sin x +2sin x cos x #160; ) dx 3∫sin x +∫sin 2x #160; dx #160; #160; #160; #160; #160; ...

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Parametric Differentiation

∫sin x 3+2cos...

Question

$\int sin x (3 + 2 cos x) d x$

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Solution

$\int sin x (3 + 2 cos x) d x$
$\int (3 sin x + 2 sin x cos x) d x$
$3 \int sin x + \int sin 2 x d x$ $[∵ 2 sin x cos x = sin 2 x]$
$= 3 (- cos x) + \frac{(- cos 2 x)}{2} + c$
$= - 3 cos x - \frac{- cos 2 x}{2} + c$
Hence, the answer is $- 3 cos x - \frac{cos 2 x}{2} + c .$

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