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Question

0logx1+x2dx

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Solution

0logx1+x2dx
=ln(x)(xi)(x+i)dx
=iln(x)2(x+i)iln(x)2(xi)dx
=ln(iu+1)udu+ln(i)1udu
=ln(1v)vdv
ln(iu+1)udu+ln(i)1udu
=ln(1iu)u+ln(i)udu
i2ln(x)x+idxi2ln(x)xidx
=iln(i)ln(|x+i|)2iln(i)ln(|xi|)2iLi2(i(x+i))2+iLi2(i(xi))2+C
=0

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