∫dx/sin^2(2x-3)=?

来源：学生作业帮助网编辑：作业帮时间：2024/05/04 15:25:22

∫dx/sin^2(2x-3)=?
∫dx/sin^2(2x-3)=?

∫dx/sin^2(2x-3)=?
由于dx=d(2x-3)/2
所以
Int(dx/sin(2x-3)^2)
=Int(d(2x-3)/sin(2x-3)^2)/2
=-cot(2x-3)/2+C

(tanx)'=(secx)^2
(cotx)'=-(cscx)^2
d(2x-3)=2dx
∫dx/sin^2(2x-3)=1/2∫csc^2(2x-3) d(2x-3)=-1/2*cot(2x-3)+C

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