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Question

31(tan1xx2+1+tan1x2+1x)dx

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Solution

I31(tan1xx2+1+tan1x2+1x)dx....................(1)
Now, tan1xx2+1+tan1x2+1x=tan1xx2+1+x2+1x1(xx2+1×x2+1x)
=tan1()=π2.
From (1),I=31π2dx.
=π2[x]31=π2[3+1]=π2×4=2π Ans

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