∫ sect dt = ∫ 1/cost dt = ∫ cost /[1-(sint)^2] dt u = sint= ∫ 1/(1-u^2) du = (1/2) ∫ [ 1/(1-u) + 1/(1+u) ] du= (1/2) ln (1+u)/(1-u) + C = (1/2) ln [(1+u)^2/(1-u^2)] + C= ln |(1+sint)/cost| + C = ...