Calc1.3

$\int x\sin(x)\,dx\,$

$\int u \,dv = uv-\int v \,du\,$

Integrate by parts. Integration by parts is a method to move derivatives from one part of the integrand to the other. To evaluate the integral, move a derivative on to the x term.

$u = x, dv=\sin(x)\,dx\,$

$du=dx, v=-\cos(x)\,$

$uv-\int v \,du = -x\cos(x)+\int \cos(x) \,dx = -x\cos(x) + \sin(x)\,$

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