" 6."quad tan^(-1)(1)/(sqrt(x^(2)-1)),|x|>1

tan^(- 1)(1/(sqrt(x^2-1))),|x|gt1

"tan"^(-1)1/(sqrt(x^(2)-1))|x|gt1

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

tan[2Tan^(-1)((sqrt(1+x^(2))-1)/x)]=

tan[(sqrt(1+x^(2))-1)/x] =

IfI=int(dx)/(x^(3)sqrt(x^(2)-1)), then Iequals a.(1)/(2)((sqrt(x^(2)-1))/(x^(3))+tan^(-1)sqrt(x^(2)-1))+C b.(1)/(2)((sqrt(x^(2)-1))/(x^(2))+x tan^(-1)sqrt(x^(2)-1))+Cc(1)/(2)((sqrt(x^(2)-1))/(x^(2))+tan^(-1)sqrt(x^(2)-1))+Cd(1)/(2)((sqrt(x^(2)-1))/(x^(2))+tan^(-1)sqrt(x^(2)-1))+C

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

Prove that tan^(-1)((sqrt(1+x^2)-1)/x)=1/2 tan^(-1)x .

Differentiate tan^(-1)((1+2x)/(1-2x))wdotrdottsqrt(1+4x^2) and tan^(-1)((sqrt(1+x^2)-1)/x) with respect to tan^(-1)(x)