`int 1/(cosx+sqrt3sinx) \ dx` equals (i) `log(tan (x/2+pi/12))+c` (ii) `log(tan (x/2-pi/12))+c` (iii) `1/2*log(tan (x/2+pi/12))+c` (iv) `1/2*log(tan (x/2-pi/12))+c`

int(1)/(cos x+sqrt(3)sin x)dx equals ( i )log(tan((x)/(2)+(pi)/(12)))+c( (ii) log(tan((x)/(2)-(pi)/(12)))+c( iii) (1)/(2)*log(tan((x)/(2)+(pi)/(12)))+c( iv )(1)/(2)*log(tan((x)/(2)-(pi)/(12)))+c

int(dx)/(cos x+sqrt(3)sin x) equals: (1)(1)/(2)log tan((x)/(2)+(pi)/(12))+c(1)/(2)log tan((x)/(2)-(pi)/(12))+c log tan ((x)/(2)+(pi)/(12))+cquad log tan((x)/(2)-(pi)/(12))+c

int(1)/(sin x+sqrt(3)cos x)dx=(1)/(2)log tan((x)/(2)+(pi)/(3))+c

int_(0)^((pi)/(2))log(tan x)*dx

int_(0)^(pi//2) log (tan x ) dx=

int_(0)^((pi)/(2))sin2x*log(tan x)dx=

int(1)/(1-cos x-sin x)dx=log|1+(cot x)/(2)|+C(b)log|1-(tan x)/(2)|+C (c) log|1-(cot x)/(2)|+C(d)log|1+(tan x)/(2)|+C

int_0^1 log(sqrt(1+x)+sqrt(1-x))dx= (A) 1/2(log2-pi/2+1) (B) 1/2(log2+pi/2+1) (C) 1/2(log2+pi/2-1) (D) none of these

int(x+sinx)/(1+cosx)dx= (A) xtan(x/2)+c (B) log(1-cosx)+c (C) (tan(x/2))/2+c (D) none of these