int_(an^(-1))^(cot^(-1)lambda)(tan x)/(tan x+cot x)dx,AA lambda in R" can not take the value "

The int_(tan^(-1)alpha)^( cot^(-1)alpha)(tan x)/(tan x+cot x)dx alpha in R cannot take the value (i) pi(ii)(pi)/(2)(iii)(pi)/(4)(iv)-(pi)/(4)

int (tan x + cot x) dx

int(tan x)/(cot x)dx

int (tan x +cot x)^(2)dx

tan^(-1)(cot x)+cot^(-1)(tan x)

cot(tan^(-1)x+cot^(-1)x)

tan^(-1) (cot x) +cot^(-1)(tan x) =

int(tan^(-1)x-cot^(-1)x)/(tan^(-1)x+cot^(-1)x)dx equals

int_(0)^((pi)/(2))(a tan x+b cot x)/(tan x+cot x)dx=