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(x+2)/((x^(2)+3x+3)sqrt(x+1))dx is equal to a) (1)/(sqrt(3))tan^(-1)((x)/(sqrt(3)(x+1))) b) (2)/(sqrt(3))tan^(-1)((x)/(sqrt(3(x+1)))) c) (2)/(sqrt(3))tan^(-1)((x)/(sqrt(x+1))) d)None of these

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

If int (sinx)/(sin^(2)x+4cos^(2)x)dx=-(1)/(sqrt(3))tan^(-1)((sqrt(3))/f(x))+c ,then f(x) equals :