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Integrals — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSIntegrals1 Mark
Question
Find $\int x \cos x d x$
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Answer

Put f (x) = x (first function) and g (x) = cos x (second function).
Then, integration by parts gives
$\int x \cos x d x=x \int \cos x d x-\int\left[\frac{d}{d x}(x) \int \cos x d x\right] d x$ 
= $x \sin x-\int \sin x d x=x \sin x+\cos x+\mathrm{C}$ 

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