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Is this correct:integral: 1/(1+cos(x)+sin(x)) dxt = tan(x/2)

  1. Jul 29, 2010 #1
    Is this correct:

    integral: 1/(1+cos(x)+sin(x)) dx

    t = tan(x/2) --> x = 2arctan(t) --> dx = 2/(1+t^2) dt

    sin(x) = 2t/(1+t^2)
    cos(x) = (1-t^2)/(1+t^2)

    1/(1+cos(x)+sin(x)) dx

    = ...

    = 2 integral 1/(2(1+t)) dt = integral 1/(1+t) dt = ln (1+t) = ln(1+tan(x/2))
     
  2. jcsd
  3. Jul 29, 2010 #2

    arildno

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    Re: Integral

    Try to differntiate your putative answer! :smile:
     
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