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Integrate[(a + b*x + c*x^2 + d*x^3)/(-1 + x^4), x] ==
(-2*(a - c)*ArcTan[x] + (a + b + c + d)*Log[-1 + x] - a*Log[1 + x] + b*Log[1 + x] - c*Log[1 + x] + d*Log[1 + x] - b*Log[1 + x^2] + d*Log[1 + x^2])/4 

                       2      3
          a + b x + c x  + d x
Integrate[---------------------, x] == 
                       4
                 -1 + x

(-2 (a - c) ArcTan[x] + (a + b + c + d) Log[-1 + x] - 
 
    a Log[1 + x] + b Log[1 + x] - c Log[1 + x] + 
 
                              2               2
    d Log[1 + x] - b Log[1 + x ] + d Log[1 + x ]) / 4
Time to compute: 0.06 second
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