Evaluate: `int(1-tanx)/(1+tanx)\ dx`

Explanation

`frac{1-tan x}{1+tan x}=frac{1-frac{sin x}{cos x}}{1+frac{sin x}{cos x}}=frac{cos x-sin x}{cos x+sin x}=frac{cos x cos (frac{pi}{4})-sin x sin (frac{pi}{4})}{cos x cos (frac{pi}{4})+sin x sin (frac{pi}{4})}`

`=cot (x+frac{pi}{4}) `

`text { Note that } sin (frac{pi}{4})=cos (frac{pi}{4})=frac{1}{sqrt{2}}`