(sec^(2)x)/((1+tan x)(2+tan x))

int(sec^(2)x)/(log(tan x)^(tan x)dx)

f((2tan x)/(1+tan^(2)x))=((cos2x+1)(sec^(2)x+tan x))/(2) then f(x)=

The integral int(sec^(2)x)/((sec x+tan x)^((9)/(2)))dx equals (for some arbitrary constant K)-(1)/((sec x+tan x)^((11)/(2))){(1)/(11)-(1)/(7)(sec x+tan x)^(2)}+K(1)/((sec x+tan x)^((11)/(2))){(1)/(11)-(1)/(7)(sec x+tan x)^(2)}+K-(1)/((sec x+tan x)^((11)/(2))){(1)/(11)+(1)/(7)(sec x+tan x)^(2)}+K

int(x^(2)(x sec^(2)x+tan x))/((x tan x+1)^(2))

sec^(2)2x=1-tan2x

sec^(2)2x=1-tan2x

int(4sec^(2)x tan x)/(sec^(2)x+tan^(2)x)dx=log|1+f(x)|+C

Evaluate: (i) int(tan x sec^(2)x)/((a+b tan^(2)x))dx (ii) int sec^(3)x tan xdx

If quad (2tan x)/(1+tan^(2)x))=((cos2x+1)(sec^(2)x+2tan x))/(2) then domain and range of y=f(x) are given by

f((2tan x)/(1+tan^(2)x))=((cos2x+1)(sec^(2)x+2tan x))/(2) then f((1)/(4))=