Calc1.3

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\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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