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(1 - tan2x)/(1 + tan2x) = (1 - sin2x/cos2x)/(1 + sin2x/cos2x) = (cos2x - sin2x)/(cos2x + sin2x) = (cos2x - sin2x)/1 = (cos2x - sin2x) = cos(2x)
d/dx (sin x + sin 2x) = cos x + 2cos 2x
sin2x + c
http://wiki.answers.com/Q/Intgration_of_sin2x=-(cos 2x)/2
1 - sin2x(1+ cos2x)/2