`int 2^-x tan h 2^(1-x) dx=`

If 2int_0^1 tan^(-1)x dx= int_0^1 cot^(-1)(1-x+x^2) dx then int_0^1 tan^(-1)(1-x+x^2) dx=

int (tanx)/(1+tan^(2)x)dx=

int 1/((1+x^2)tan^(-1)x)dx

int (1-tan^2x)/(1+tan^2x) dx

int (1-tan^2x)/(1+tan^2x) dx

int e^x(1 + tan x + tan^2x) dx =

int (e^(x) (x^(2) tan^(-1) x + tan^(-1) x + 1))/( x^(2) + 1) dx is

(i) int (tan^-1 x)^2/(1+x^2) dx (ii) int (e^(sin^-1 x))/sqrt(1-x^2)dx (iii) int (sec^2(2tan^-1 x))/(1+x^2) dx

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

int e^(tan^-1x)/(1+x^2)^2dx