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Integrate the following expression with respect to x by parts: (2x)sin(x)

The integration by parts formula: S:udv/dx = uv - S:v*du/dx, where S: means "Integral of with respect to x"

Let 2*x be u and sin(x) be dv/dx

So du/dx =2 and v= -cos(x)

So S:(2x)sin(x) = (2x)(-cos(x)) - S:-cos(x)*2

= -2xcos(x) + 2*sin(x)

= 2sin(x) - 2x*cos(x) +c

DP

Answered by David P. • Maths tutor

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