" 1."3e^(x)-(1)/(5x)+sec x*tan x

Evaluate : int "("3e^(x) -(1)/(5x)+ " sec x tan x ) dx "

Evaluate : int "("3e^(x) -(1)/(5x)+ " sec x tan x ) dx "

int3e^(x)-(1)/(5x)+sec x*tan xdx

int(3e^(x)-(1)/(5x)+sec x-tan x)dx

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

If sec x=x+(1)/(4x) then sec x+tan 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

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

Differentiate the following functions with respect to x(2x+3)/(x^(2)-5) (ii) (x+3)/(x^(2)+1) (iii) (1+tan x)/(1-tan x) (iv) (sec x+tan x)/(sec x-tan x)