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Proof: Integral cot(x)
(Math | Calculus | Integrals | Table Of | cot x)
 
Discussion of
(integral) cot x = ln|sin x| + C.

1. Proof

    Strategy: Make in terms of sin's and cos's; Use substitution.
     
    (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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