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D/Dx(Cotx)等于多少

d(cotx)/dx =(cotx)' =-csc²x

∫[cotx/(sinx)^2]dx =∫[(cosx/sinx)/(sinx)^2]dx =∫[cosx/(sinx)^3]dx =∫[1/(sinx)^3]d(sinx) =-(1/2)[1/(sinx)^2]+C =-1/[2(sinx)^2]+C =-1/(1-cos2x)+C =1/(cos2x-1)+C.

解:设定积分值为w w=[0,π/2]∫2/(1+(tanx)^a)dx /**/方括号表示积分限 = [0,π/2]∫[2/(tanx)^a]/[1/(tanx)^a+1]dx = [0,π/2]∫2*(cotx)^a/[(cotx)^a+1]dx 作变量代换 u=π/2 -t ==> t= π/2 -u, 积分式化为: w= [π/2,0]∫2*[cot(π/2-u]^a/[(cot(π/2-...

= (-1/7)cot^7(x) + (1/5)cot^5(x) - (1/3)cot³x + cotx ...标准方法是拆开被积函数:∫ cot^8(x) dx=∫ cot^6(x) * cot^2x d.....

原式=∫cot²x·csc²x·csc²x·dx =∫cot²x·(1+cot²x)·csc²x·dx =∫cot²x·(1+cot²...

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