∫上限1下限1/根号2 根号（1-x^2)/x^2dx
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∫(1/√2到1) √(1-x²) / x² dx
令x=sinψ => dx=cosψ dψ
当x=1/√2，ψ=π/4 // 当x=1，ψ=π/2
原式= ∫(π/4到π/2) cosψ/sin²ψ * cosψ dψ
= ∫(π/4到π/2) cot²ψ dψ
= ∫(π/4到π/2) (csc²ψ-1) dψ
= (-cotψ - ψ)[π/4到π/2]
= (0-π/2)-(-1-π/4)
= -π/2+1+π/4
= 1-π/4
令x=sinψ => dx=cosψ dψ
当x=1/√2，ψ=π/4 // 当x=1，ψ=π/2
原式= ∫(π/4到π/2) cosψ/sin²ψ * cosψ dψ
= ∫(π/4到π/2) cot²ψ dψ
= ∫(π/4到π/2) (csc²ψ-1) dψ
= (-cotψ - ψ)[π/4到π/2]
= (0-π/2)-(-1-π/4)
= -π/2+1+π/4
= 1-π/4
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