Evaluate: (i) `int(secx)/(log(secx+tanx)\ dx` (ii) `int(cos e c\ x)/(logtan(x/2))\ dx`

Explanation

(i)


Note: Here, we are considering `log x` as `log _{e} x`

`Let {I}=int frac{sec x}{log (sec x+tan x)} d x`

Putting `log (sec x+tan x)=t Rightarrow frac{sec x tan x+sec ^{2} x}{sec x+tan x}=frac{d t}{d x}`

`Rightarrow sec x frac{(sec x+tan x)}{sec x+tan x}=frac{d t}{d x}`

`Rightarrow sec {xdx}=d t`

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