If ∫x+1×2+x+1dxx2+x+1=kx−1×2+x+1+C then the value of k

If x+1x2+x+1dxx2+x+1=kx1x2+x+1+C then the value of k

  1. A

    1/2

  2. B

    1/3

  3. C

    2/3  

  4. D

    none of these 

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    Solution:

    Differentiating both the sides w.r.t.x, and simplifying , we get 

    x+1x2+x+13/2=3k2x+1x2+x+13/2k=23

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