Themes > Science > Mathematics > Calculus > Integrals > Integrals Table > Integral cot(x)

Discussion of (integral) cot x = ln|sin x| + C.


1. Proof

    Strategy: Make in terms of sin's and cos's; Use Subtitution.
     
    (integral) cot x dx = (integral) cos x 

    sin x

    		 dx
    set
      u = sin x.
    then we find
      du = cos x dx

    substitute du=cos x, u=sin x
     
    (integral) cos x 

    sin x

    		 dx = (integral)
    du 

    u

    solve integral

    = ln |u| + C

    substitute back u=sin x

    = ln |sin x| + C
    Q.E.D.


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