Evaluate: (i) `int(1+tanx)/(x+logsecx)\ dx` (ii) `int(sin2x)/(a^2+b^2sin^2x)\ dx`

Explanation

(i)

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

`Let {I}=int frac{1+tan x}{x+log sec x} d x`

Putting `x+log sec x=t`

`Rightarrow 1+frac{sec x tan x}{sec x}=frac{d t}{d x}`

`Rightarrow(1+tan x) d x=d t`

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

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