x = tant,dx = sec²t dt
∫ (sec²tdt)/(tan^4t + tan^6t)
= ∫ (sec²t)/(tan^4t•sec²t) dt
= ∫ cot⁴t dt
= ∫ cot²t•(csc²t - 1) dt
= ∫ cot²t•csc²t dt - ∫ cot²t dt
= -∫ cot²t d(cott) - ∫ (csc²t - 1) dt
= (-1/3)cot³t + cott + t + C
= (-1/3)(1/x)³ + 1/x + arctan(x) + C
= -1/(3x³) + 1/x + arctan(x) + C