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Question
Find the integrals of the function:
`(cos 2x+ 2sin^2x)/(cos^2 x)`
Solution
Let `I = int (cos 2x + 2 sin^2)/cos^2 x dx`
`= int ((cos^2 x - sin^2 x) + 2 sin^2 x)/cos^2 x` .... [∵ cos 2x = cos2 x - sin2 x]
`= int(cos^2x + sin^2x)/cos^2 x dx`
`= 1/cos^2 x dx`
`= int sec^2 x dx = tan x + C`
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