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Question

Integrate the function xlog2x

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Solution

Let I=xlog2xdx
Taking log2x as first function and x as second function and integrating by parts, we obtain
I=log2xxdx{(ddxlog2x)xdx}dx
=log2xx2222xx22dt
=x2log2x2x2dx
=x2log2x2x24+C

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