" 37."sqrt(tan^(-1)((x)/(2)))

tan^(-1)(x+sqrt(1+x^(2)))=

int(1)/(1+cos^(2)x)dx=(1)/(sqrt(2))tan^(-1)((tan x)/(sqrt(2)))+c

int(1)/(7+5cos x)dx=(1)/(sqrt(6))tan^(-1)((1)/(sqrt(6))(tan x)/(2))+C(b)(1)/(sqrt(3))tan^(-1)((1)/(sqrt(3))(tan x)/(2))+C(c)(1)/(4)tan^(-1)((tan x)/(2))+C(d)(1)/(7)tan^(-1)((tan x)/(2))+C

int(dx)/(sin^(2)x+Tan^(2)x)=(-1)/(l)cot x-(1)/(k sqrt(2))Tan^(-1)((tan x)/(sqrt(2)))+c then (k)^l=

int(dx)/(sin^(2)x+tan^(2)x)=(-1)/(l)cot x-(1)/(k sqrt(2))Tan^(-1)((tan x)/(sqrt(2)))+c then (k)^l=

Differentiate tan^(-1) ((sqrt(1+x^(2))-1)/(x)) w.r.t. tan^(-1) ((x)/(sqrt(1-x^(2)))) .

If 3 tan ^(-1)((1)/(2+sqrt(3)))-tan ^(-1) (1)/(x)=tan ^(-1) (1)/(3) then x=

int (dx)/((x + 1) sqrt(x)) is equal to a) tan^(-1) sqrt(x) + C b) 2 tan^(-1) x + C c) 2 tan^(-1) (sqrt(x)) + C d) tan^(-1) (x^((3)/(2))) + C

Differentiate tan^(-1)x/(1+sqrt((1-x^2))) +{2tan^(-1)sqrt(((1-x)/(1+x)))}sinwdotrdottdotxdot