`intcos(2cot^(-1)sqrt((1-x)/(1+x)))dx=`

int cos (2 cot^-1 sqrt((1-x)/(1+x)))dx

int cos[2cot^(-1)sqrt((a-x)/(a+x))]dx

intcos{2tan^(-1)sqrt((1-x)/(1+x))}dx is equal to

If I=int_(0)^(1) cos{ 2 "cot"^(-1)sqrt((1-x)/(1+x))}dx then

cot^(-1)((sqrt(1-x^(2)))/(x))

Differentiate w.r.t. as indicated : tan^(-1)(x/(1+sqrt(1-x^(2))))" w.r.t. "sin(2cot^(-1)sqrt((1+x)/(1-x)))

cot^(-1)(sqrt(1+x^2)-x)

(d)/(dx)[sin^(2)cot^(-1)sqrt((1-x)/(1+x))] is