Problem

Using integration by parts find $\int x \sin x \mathrm{~d} x$.

Answer

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Answer

Apply integration by parts formula: \(\int x \sin x \mathrm{~d} x = -x\cos x + \sin x + C\)

Steps

Step 1 ：Choose u = x and dv = \(\sin x \mathrm{~d} x\), then find du and v: du = \(\mathrm{d} x\), v = -\(\cos x\)

Step 2 ：Apply integration by parts formula: \(\int x \sin x \mathrm{~d} x = -x\cos x + \sin x + C\)

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