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# Integrate the functions x sin x

Q1  Integrate the functions $x \sin x$

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Given function is
$f(x)=x \sin x$
We will use integrate by parts method
$\int x\sin x = x.\int \sin xdx - \int(\frac{d(x)}{dx}.\int sin x dx)dx\\ \\ \int x\sin x = x.(-\cos x)- \int (1.(-\cos x))dx\\ \\ \int x\sin x= -x\cos x+\sin x + C$
Therefore, the answer is $-x\cos x+\sin x + C$

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