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Question

Prove that dx(1+x)(1+x2)=12log(1+x)+14log(1+x2)+12tan1x.

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Solution

1(x+1)(x2+1)dx=(1x2(x2+1)+12(x1))dx
=121xx2+1dx+121x+1dx
=12(1x2+1xx2+1)dx+121x+1dx
=12xx2+1dx+121x2+1dx+121x+1dx
=14log(x2+1)+12tan1x+12log(x+1)

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