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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-...

在这里使用分部积分法即可, ∫ arctanx dx = x * arctanx - ∫ x d(arctanx) = x * arctanx - ∫ x/(1+x²) dx = x * arctanx - (1/2)∫ d(x²)/(1+x²) = x * arctanx - (1/2)∫ d(1+x²)/(1+x²) = x * arctanx - (1/2)ln(1+x...

∫ x*csc^2x*cot^2x dx =(1/3)*∫ x*(3*csc^2x*cot^2x) dx =(1/3)*∫ x d(cot^3x) ……凑微分法 =(1/3)*x*cot^3x - (1/3)*∫ cot^3x dx ……分部积分法 =(1/3)*x*cot^3x - (1/3)*∫ cos^3x/sin^3x dx =(1/3)*x*cot^3x - (1/3)*∫ cos^2x/sin^3x d(sinx) ……...

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