[" 3) "int(dx)/(1+tan x)=],[[" (a) "log(x+sin x)," (b) "log(sin x+cos x)],[" (c) "2sec^(2)(x)/(2)," (d) "(1)/(2)[(x+log(sin x+cos x)]]]

int(1)/(1+tan x)dx=(log)_(e)(x+sin x)+C(b)(log)_(e)(sin x+cos x)+C(c)2(sec^(2)x)/(2)+C(d)(1)/(2){x+log(sin x+cos x)}+C

(d)/(dx) [(x)/(2) + 1/2 log | sin x + cos x|]=

int (ln (tan x)) / (sin x cos x) dx

int(log(tan x))/(sin x cos x)dx=

int sin x log(cos x)dx

" Prove that " : int(2 sin x +3 cos x)/(3sin x+4 cos x) dx = (18x)/(25) +(1)/(25)log|3s sin x+ 4cosx|c

int (cos x)/( sin x log sin x)dx=

If y=(sin x)^(tan x), then (dy)/(dx)= (a) (sin x)^(tan x)(1+sec^(2)x log sin x)(b)tan x(sin x)^(tan x-1)cos x(c)(sin x)^(tan x)(d)sec^(2)x log sin x tan x(sin x)^(tan x-1)

(i) int (1+ tan x)/(x +log sec x) dx (ii) int (1+ cot x)/(x+log sin x) dx.