令 x=2t,则 dx = 2dt,sinx = sin(2t) = 2 sint cost ∫ dx / (1 + sinx)= ∫ 2dt / (sin²t + cos²t + 2 sint cost)= ∫ 2dt / (sin t + cos t)²= ∫ 2dt / [√2 sin (t + π/4) ]²= ∫ csc
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