Mark the correct alternative in each of the following:

Question:

Mark the correct alternative in each of the following:

If $\int x \sin x d x=-x \cos x+\alpha$, then $\alpha$ is equal to

A. $\sin x+C$

B. $\cos x+C$

C. $\mathrm{C}$

D. none of these

Solution:

using integration by parts

$I=\int x \sin x d \square$

$\left.=x \int \sin x d x-\int \frac{d x}{d x}(x) \int \sin x\right)$

$I=x \cos x+\int \cos x d x$

$\left(\because \int \sin x=-\cos x\right)$

$=x \cos x+\sin x+c$

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