(1 + 2 x^2) / [ (1 + x^2) * x^4] = 1 / x^4 + 1/ x^2 - 1/(1+x^2)
∫ (1 + 2 x^2) / [ (1 + x^2) * x^4] dx
= ∫ [1 / x^4 + 1/ x^2 - 1/(1+x^2)] dx
= (-1/3) x^(-3) - 1/x - arctanx + C