integrals.wolfram.com   Use one of Mathematica's 2500+ functions FREE online

Integrate[(2 + x + x^2 + x^3)/(2 + 3*x^2 + x^4), x] ==
ArcTan[x] + Log[2 + x^2]/2

                   2    3
          2 + x + x  + x
Integrate[---------------, x] == 
                  2    4
           2 + 3 x  + x

                     2
            Log[2 + x ]
ArcTan[x] + -----------
                 2