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

int(cotx+cot^3x)/(1+cot^3x)dx

If phi(x)=intcot^(4)x dx+(1)/(3)cot^(3)x-cotx and phi((pi)/(2))=(pi)/(2) then phi(x)=

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

If: cotx + cot(pi/4 +x)=2 , then: x=