[" (19) "e^(sqrt(1-x^(2)))tan x,," 20."]

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

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

int(e^(x+a)-(1)/(sqrt(1-x^(2)))+tan^(2)x)dx :e^(x+a)-sin^-1x+tan^2x-x+C

sqrt((1-tan x)/(1+tan x))

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

If y = tan^(-1) {(x)/(1 + sqrt(1 - x^(2)))} + sin { 2 tan^(-1) sqrt((1 - x)/(1 + x))}, "then" (dy)/(dx) =

(d)/(dx) {Tan ^(-1)"" (sqrt(1+ x ^(2))+ sqrt(1- x ^(2)))/( sqrt(1+ x ^(2))- sqrt(1- x ^(2)))}=

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