令x = secz,0 < z < π/2 或 π/2 < z < π
dx = secz tanz dz
当x = -2,z = 2π/3；当x = -√2,z = 3π/4
即z ∈ [2π/3,3π/4],∴π/2 < z < π
∫[-2,-√2] dx/√(x² - 1)
= ∫[2π/3,3π/4] (secz tanz)/(-tanz) dz
= ∫[3π/4,2π/3] secz dz
= ln|secz + tanz|_[3π/4,2π/3]
= ln(sec(2π/3) + tan(2π/3)) - ln(sec(3π/4) + tan(3π/4))
= ln[(2 + √3)/(1 + √2)]
≈ 0.43558...