Find the integral of int x sin x dx by method o... - SS3 Mathematics Integral Calculus (Integration) Question
Find the integral of \(\int_{}^{}x\sin x\ dx\) by method of integration by parts
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\[\int_{}^{}u\ dv = uv - \ \int_{}^{}v\ du\]
\(u = x\), \(du = 1\)
\(dv = \sin x\), \(v = - \cos x\)
\[\int_{}^{}x\sin x\ dx = - x\cos x - \ \int_{}^{}{- \cos x}\]
\[= - x\cos x + \int_{}^{}{\cos x}\]
\[= - x\cos x + \sin x\]
\[= \sin x - x\cos x\]
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