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Question

Solve : 0xlnx(1+x2)2

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Solution

xlnx(1+x2)2dx

Integration by parts

=lnx2(1+x2)12x(1+x2)dx

=lnx2(1+x2)(12((ln|x|)12(ln|x2+1|)))

xlnx(1+x2)2dx=lnx2(1+x2)+12((ln|x|)12(ln|x2+1|))+C

0xlnx(1+x2)2dx=00=0

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