[int(dx)/(cos x+sqrt(3)sin x)" equals- "],[[" 1) "(1)/(2)log tan((x)/(2)+(pi)/(12))+C," 2) "(1)/(2)log tan((x)/(2)-(pi)/(12))+c],[" 3) "log tan((x)/(2)+(pi)/(12))+c," 4) "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)/(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)/(cosx+sqrt(3)sinx) equals: (1) 1/2logtan(x/2+pi/(12))+c (2) 1/2logtan(x/2-pi/(12))+c (3) logtan(x/2+pi/(12))+c (4) logtan(x/2-pi/(12))+c

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

int(dx)/(cosx-sinx) is equal to a) (1)/(sqrt(2))log|tan(pi/2-pi/8)|+c b) (1)/(sqrt(2))log|cot(x/2)|+c c) (1)/(sqrt(2))log|tan(pi/2-(3pi)/(8))|+c d) (1)/(sqrt(2))log|tan(x/2+(3pi)/(8))|+c

intdx/(cosx-sinx) is equal to (A) 1/sqrt(2)log|tan(x/2-(3x)/8)|+C (B) 1/sqrt(2)log|cot(x/2)|+C (C) 1/sqrt(2)log|tan(x/2-pi/6)|+C (D) 1/sqrt(2)log|tan(x/2+(3pi)/8)|+C

The general solution of the differential equation (dy)/(dx)+sin((x+y)/(2))=sin((x-y)/(2)) is (a) log tan((y)/(2))=C-2sin((x)/(2))(c)log tan((y)/(2)+(pi)/(4))=C-2sin x(d) Non of log tan((y)/(2)+(pi)/(4))=C-2sin x(d) Non of these

int(dx)/(sqrt(3)sin x+cos x)=A log_(e)tan(Bx+c)+K then (A)A=(1)/(2)(B)B=-(1)/(2)(C)C=(pi)/(12) (D) C=(pi)/(4)

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

int _(0) ^(pi//2) (cos x )/( 1 + sin x ) dx equals to a) log 2 b) 2 log 2 c) (log2) ^(2) d) 1/2 log 2