evaluate dx/1+x^4

I = 1/1+x⁴ dx

2I =  2/1+x⁴ dx

divide num & denominator by x²

    =2/x² /(x²+1/x²) dx

    =[1/x²+1 + 1/x²-1 ]/(x²+1/x²) dx

    =(1/x²+1)dx/x²+1/x²  +  (1/x²-1)dx/(x²+1/x²)

    =(1+1/x²)dx/{(x-1/x)² + 2} + -(1-1/x²)dx/{(x+1/x)² - 2}

               I                                          II

put x-1/x = t in first &  x+1/x = u in second & then 

2I =         dt/t²+2                 +          -du/u²-2

2I =         tan^-1(t/2^1/2) / 2^1/2        +  -log(u-2^1/2/u+2^1/2)/8^1/2 + C

now put  t , u in above eq...