Integration of 1/(1+cos^2 x) ?!..

Dear Student,

Let I = 11 + cos2x dx  = 1cos2x1cos2x + 1 dx = sec2xsec2x + 1 dx =sec2x1 + tan2x + 1 dxI = sec2xtan2x + 2 dxput tan x = tsec2x dx = dtso, I = 1t2 + 22 dt = 12 tan-1t2+c=  12 tan-1tanx2+c
Regards.

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