令x=2sint，则dx=2costdt
原式=∫(0,π/2) 2costdt/(2+2cost)
=∫(0,π/2) costdt/(1+cost)
=∫(0,π/2) [cos^2(t/2)-sin^2(t/2)]dt/2cos^2(t/2)
=(1/2)*∫(0,π/2) [1-tan^2(t/2)]dt
=(1/2)*∫(0,π/2) [2-sec^2(t/2)]dt
=∫(0,π/2) [2-sec^2(t/2)]d(t/2)
=[t-tan(t/2)]|(0,π/2)
=π/2-1
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