22. (i) dx. 1- tan x ch (N.C •dx

(d)/(dx)((1-tan x)/(1+tan x))*(d)/(dx)((1-tan x)/(1+tan x))

Evaluate: (i) int(1+tan x)/(1-tan x)dx (ii) int(cos x)/(cos(x-a))dx

int ("tan"x)/(1 + tan x )dx

" (.) "int(tan x)/(1+tan x)dx

I= int(1)/(sec x-tan x)dx

If I_n = int tan^n x dx , then prove that I_n = (tan^(n-1) x)/(n - 1) - I_(n - 2) . Hence find int tan^7 x dx

(i) int x sin^-1 x dx (ii) int x cos^-1 x dx (iii) int x tan^-1 x dx (iv) int x cot^-1 x dx

∫tan^(-1) (sec x + tan x) dx