The integral can be written as :
(1/2)*[

(x
2+1) dx/(1+x
4) -

(x
2-1) dx/(1+x
4) ]
Call the first integral , I1 and the second integral I2
Divide by x2 (numerator and denominator) in both the integrals.
If u need help in proceeding, plz reply.
Cheers.