∫(1,√3) dx/(x^2√(1+x^2))
换元，x=tant
=∫(π/4,π/3) d(tant)/(tan^2t√(1+tan^2t))
=∫(π/4,π/3) (1/cos^2t)/(tan^2t*(1/cost)) dt
=∫(π/4,π/3) cost/sin^2t dt
=∫(π/4,π/3) sin^(-2)t d(sint)
=-sin^(-1)t | (π/4,π/3)
=2-2√3/3
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