Evaluate: (i) `int(sec^2x)/(tanx+2)\ dx` (ii) `int(2cos2x+sec^2x)/(sin2x+tanx-5)\ dx`

Explanation

(i)

`text { Let } {I}=int frac{sec ^{2} x}{tan x+2} d x `

`text { Putting } tan x=t `

`Rightarrow sec ^{2} x=frac{d t}{d x} `

`Rightarrow sec ^{2} x d x=d t `

`therefore I=int frac{1}{t+2} d t `

`=ln |t+2|+C `

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