If `int(co sec x+cot x-1)/(1+cot x-cos ecx)dx=2ln|f(x)|+c` and `f((pi)/(2))=(1)/(sqrt(2))` then the nearest integer value of `2sqrt(3)f((pi)/(3))` is equal to

int(sec x cos ecx)/(log cot x)dx

int sqrt(1+2cot x(cot x+cos ecx))dx

sqrt(1+2cot x(cos ecx+cot x))dx=

If f(x)=(1)/(3)cot^(3)x-cot x+int(cot^(4)x)dx and f((pi)/(2))=(pi)/(2) then f(x)=

If f(x)=cos ec(x-(pi)/(3))cos ec(x-(pi)/(6)) then the value of int_(0)^((pi)/(2))f(x)dx is

f(x)=int x^(sin x)(1+x cos x*ln x+sin x)dx and f((pi)/(2))=(pi^(2))/(4) Then the value of |cos(f(pi))| is

If cos ecx=(2)/(sqrt(3)) and cot x=(-1)/(sqrt(3))x in[0,2 pi], then the value of cos x+cos2x+cos3x is equal to

If int_(0)^( pi/2)(cot x)/(cot x+cos ecx)dx=m(pi+n) then m*n is equal to :

If int f(x)dx=-2cot(sqrt(x))+c ,then f(x) is equal to ?

For x in [0, (pi)/(2)] if int(tan x sqrt(sec x)(1+cos^(2)x))/(sqrt(cos x+sin^(2)x))dx=2sqrt(f(x)+1)+c and f((pi)/(3))=(3)/(2) then f((pi)/(4)) = (where[.] denotes I F)