令x = tanθ,dx = sec²θ dθ
∫(0→1) (1 + x²)^(- 3/2) dx
= ∫(0→π/4) (1 + tan²θ)^(- 3/2) · sec²θ dθ
= ∫(0→π/4) (secθ)⁻³ · sec²θ dθ
= ∫(0→π/4) cosθ dθ
= sinθ:0→π/4
= sin(π/4) - sin(0)
= √2/2
令x = tanθ,dx = sec²θ dθ
∫(0→1) (1 + x²)^(- 3/2) dx
= ∫(0→π/4) (1 + tan²θ)^(- 3/2) · sec²θ dθ
= ∫(0→π/4) (secθ)⁻³ · sec²θ dθ
= ∫(0→π/4) cosθ dθ
= sinθ:0→π/4
= sin(π/4) - sin(0)
= √2/2