换元法求积分用换元法
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换元法求积分用换元法换元法求积分用换元法换元法求积分用换元法设x=2t,则dx=2dt∫dx/(1-cosx)=∫2dt/(1-cos2t)=∫2dt/[2(sint)^2]=∫dt/(sint)^2
换元法求积分用换元法
换元法求积分
用换元法
换元法求积分用换元法
设 x = 2t,则 dx = 2dt
∫dx/(1-cosx)
=∫2dt/(1-cos2t)
=∫2dt/[2(sint)^2]
=∫dt/(sint)^2
=∫(csct)^2*dt
=-cot(t) + C
=-cost/sint + C
=-2(cost)^2/[2sint*cost] + C
=-(1+cos2t)/sin2t + C
=-1/sin2t - cos2t/sin2t + C
=-csc2t - cot2t + C
=-cscx - cotx + C
所以,答案是 D