∫ 1/x(x^4+1)dx=

let
x^2= tany
2xdx = (secy)^2 dy
∫dx/[x(x^4+1)]
=∫(2xdx)/[x^2(x^4+1)]
=∫(secy)^2 dy/[tany(secy)^2]
=∫coty dy
=ln|siny| + C
=ln |x^2/√(x^4+1)| + C