sec x+tan x)^(2)dx

The value of int_(0)^(pi/4)(sec x)/(secx + tan x)^(2).dx is

int (sec^(2)x)/((sec x+ tan x)^(5))dx=

∫tan^(-1) (sec x + tan x) dx

int(sec^(2)x)/((sec x+tan x)^((9)/(2)))dx

The integral int (sec^(2) x)/((sec x+tan x)^(9//2))dx equals : (for some arbitrary constant k)

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

Differentiate tan^(-1)(sec x+tan x),^(*)-pi/2

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

int sec^(2) x tan^(2) x dx=