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Fun integral

  1. Oct 2, 2011 #1
    A certain program, that shall remain nameless, tells me that the integral of cos(tan(θ)-2θ) from 0 to pi/2 is pi/e. Does anyone know of a variable transform or contour that would help me to derive this result? I'm really interested in integrals of the function cos(a tan(θ)-b θ), but, I'd be temporarily contented with knowing how to explicitly do the (a=1,b=2) case.
     
  2. jcsd
  3. Oct 4, 2011 #2
    See attachment :
     

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