∫cotx(cotx-cscx)dx=

∫cotx(cotx-cscx)dx=
∫cotx(cotx-cscx)dx=

∫cotx(cotx-cscx)dx=
∫cotx(cotx-cscx)dx
=∫(cos^2x-cosx)/sin^2xdx (化简得来的)
=∫(1-sin^2x-cosx)/sin^2xdx
=∫(1/sin^2x-1-cosx/sin^2x)dx
=-x+∫1/sin^2xdx-∫1/sin^2xd(sinx)
=-x+tanx+1/sinx+C

我是去打酱油的，路过

查高等数学上册后面的积分表吧

∫cotx(cotx-cscx)dx @(cotx = cosx/sinx & cscx = 1/sinx)
=∫(cosx/sinx) * [(cos-1)/sinx] dx @(sinx^2 + cosx^2 = 1)
=∫[(cosx)^2-cosx]/[1-(cosx)^2] dx
=∫-1+1/(1+cosx) dx @(1 ...

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∫cotx(cotx-cscx)dx @(cotx = cosx/sinx & cscx = 1/sinx)
=∫(cosx/sinx) * [(cos-1)/sinx] dx @(sinx^2 + cosx^2 = 1)
=∫[(cosx)^2-cosx]/[1-(cosx)^2] dx
=∫-1+1/(1+cosx) dx @(1 + cosx = [cos(x/2)]^2)
= -x + ∫[sec(x/2)]^2 dx
= -x + 2*{∫[sec(x/2)]^2 d(x/2)} @(整体：x/2)
= -x + 2tan(x/2) + C
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