Integration of x . Int. 1/(x^2 + 1) = ...?

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Answer

         -1
    x tan x + C

Explanation

If we solve it as ...

   \  /                    /
    \ |   1               /
    x |-------           /
      |      2          /
      | 1 + x          / 
      /   \           /
           \         /
         /          /
       1 |   2x    /
    = ---|------- /
      2x |      2
         | 1 + x \   
         /    /   \
             /     \
       1    /      2
    = --- ln (1 + x )   + C
      2x  /          \ 
         /            \
        /              \
       /                \

Here x is before the integration sign. 
So here we have to find only the integration of 1/(1+x^2)

      / 
      |   1
    x |-------
      |      2
      | 1 + x    
      /
            -1
    = x . tan x + C

           -1
    = x tan x + C

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