Evaluate: (i) `int(1+tanx)/(1-tanx)\ dx` (ii) `int(cosx)/(cos(x-a))\ dx`

Explanation

(i)

`text { Let } {I}=int(frac{1+tan x}{1-tan x}) d x `

`=int(frac{1+frac{sin x}{cos x}}{.1-frac{sin x}{cos x}) d x}. `

`=int(frac{cos x+sin x}{cos x-sin x}) d x `

`text { Putting } cos x-sin x=t `

`Rightarrow(-sin x-cos x) d x=d t `

`Rightarrow(sin x+cos x) d x=-d t `

...