If `int((x+2)dx)/((x^2+3x+3)sqrt((x+1))) =2/(sqrt(3))[tan^(- 1)((f(x)+1)/(sqrt(3)))+tan^(- 1)((f(x)-1)/(sqrt(3)))]+c` then f(x) is equal to

int_(th x^(2)(x))^( If )((x+2)dx)/((x^(2)+3x+3)sqrt((x+1)))=(2)/(sqrt(3))[tan^(-1)((f(x)+1)/(sqrt(3)))+tan^(-1)((f(x)-1)/(sqrt(3)))]+c

If 3tan^(-1)((1)/(2+sqrt(3)))-(tan^(-1)1)/(x)=(tan^(-1)1)/(3) then x is equal to 1(b)2(c)3(d)sqrt(2)

If int(2x-sqrt(sin^(-1)x))/(sqrt(1-x^(2)))dx=C-2sqrt(1-x^(2))-(2)/(3)sqrt(f(x)) then f(x) is equal to

If f(x) = sqrt((sqrt(x-1)-2)^2)+sqrt((sqrt(x-1)-3)^2) , then f '(2) is equal to :

If y=log sqrt((x^(2)+x+1)/(x^(2)-x+1))+(1)/(2sqrt(3)){tan^(-1)backslash(2x+1)/(sqrt(3))+tan^(-1)backslash(2x-1)/(sqrt(3))} then prove that (dy)/(dx)=(1)/(x^(4)+x^(2)+1)

If y=log sqrt((x^(2)+x+1)/(x^(2)-x+1))+(1)/(2sqrt(3)){tan^(-1)backslash(2x+1)/(sqrt(3))+tan^(-1)backslash(2x-1)/(sqrt(3))} then prove that (dy)/(dx)=(1)/(x^(4)+x^(2)+1)

int(dx)/(3+sin2x)=(1)/(sqrt(k))Tan^(-1)((3Tan x+1)/(sqrt(8)))+C where k is

If f(x)=tan^(-1)((sqrt(3)x-3x)/(3sqrt(3)+x^(2)))+tan^(-1)(x/(sqrt(3))),0lexle3, then range of f(x) is

If f(x) = sqrt((1)/(tan^(-1)(x^(2)-4x + 3))) , then f(x) is continuous for