Question

calculate the calculation of ....

Answer 1

Hi

First put $\tan x = \frac{\sin x}{\cos x}$ so that 

 $I = \int \frac{(1- \tan x)}{(1+\tan x)} \, dx = \int \frac{(\cos x- \sin x)}{(\cos x+\sin x)} \, dx$

Put ${(\cos x+\sin x) = t \Righatarrow  (- \sin x + \cos x) dx = dt[tex] so that   [tex]I = \int \frac{1}{t} \, dt = \ln(t)+c = \ln(\sin x +\cos x) +c$

Answer 2

Answer:

Refer the picture given below .