Question & Answer » Mathematics Questions » What is the Integral of Sec x

What is the Integral of Sec x

Answer:  The integral of sec x is written as a,

ln|sec x + tan x| + C

Also written as, 

 ∫ sec x dx = ln |sec x + tan x| + C.

In this formula, ‘ln’ is used for showing the natural algorithm, while ‘C’ is the integration constant. The integral of sec x is called a derivative of sec x. This is the standardised formula of integral of sec x. Otherwise, there are many formulas for the same. These are:

  • ∫ sec x dx = ln | tan [ (x/2) + (π/4) ] | + C 
  • ∫ sec x dx = (1/2) ln | (1 + sin x) / (1 – sin x) | + C
  • ∫ sec x dx = cos x-1(sec x) + C (or) sin x-1(tan x) + C (or) tan x-1(sin x) + C.