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Question

Evaluate logxx2dx.

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Solution

logxdxx2

Integrating by parts,
u.v dx=uv dx (dudxv dx)dx

Let u=logxdu=1xdx

and v=1x2

logxdxx2=logx1x2 dx (dlogxdx1x2 dx)dx

=logxx1x×1xdx

=logxx+1x2dx

=logxx1x

=1logxx+c

where c is the constant of integration.

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