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Question

(A) To solve the integral $\int x \cos x \, dx$,we use the method of integration by parts: $\int u \, dv = uv - \int v \, du$.Let $u = x$ and $dv = \c

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$x \sin x + \cos x + C$

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(A) To solve the integral $\int x \cos x \, dx$,we use the method of integration by parts: $\int u \, dv = uv - \int v \, du$.Let $u = x$ and $dv = \cos x \, dx$.Then $du = dx$ and $v = \int \cos x \, dx = \sin x$.Applying the formula: $\int x \cos x \, dx = x \sin x - \int \sin x \, dx$.Since $\int \sin x \, dx = -\cos x$,we get:$\int x \cos x \, dx = x \sin x - (-\cos x) + C = x \sin x + \cos x + C$.

$\int x \cos x \, dx = $

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