" 4."(e^(x)tan x+1)/(tan x)

int (e ^ (x) tan x + 1) / (tan x)

int e^(x)((2tan x)/(1+tan x)+cot^(2)(x+(pi)/(4)))dx is equal to e^(x)tan((pi)/(4)-x)+ce^(x)tan(x-(pi)/(4))+ce^(x)tan((3 pi)/(4)-x)+c(d) none of these

If int e ^(x) ((2tan x)/(1+tan x)+ cosec ^(2)(x+(pi)/(4)))dx =e ^(x). g(x)+k, then g ((5pi)/(4))=

e^(tan^(-1)x)log(tan x)

e^(x) sec x ( 1 + tan x )

int_(0)^(pi//4)e^(x)(1+tan x + tan^(2)x)dx=

(tan ((pi)/(4) +x))/( tan ((pi)/(4) -x ))= ((1 + tan x )/( 1- tan x )) ^(2)

(tan ((pi)/(4) +x))/( tan ((pi)/(4) -x ))= ((1 + tan x )/( 1- tan x )) ^(2)

Prove that (tan((pi)/(4)+x))/(tan((pi)/(4)-x))=((1+tan x)/(1-tan x))^(2)