What will be the value of this? Integration secxd(sec x)

1 Answer
Feb 9, 2018

sec^2 x - 1/2 tan^2 x +C

Explanation:

This is integration of the product of two functions. One is sec x and the other is d/dx (secx)

Let first function be secx and the second function be d/dx (sec x).

Application of the product rule of integration is:

first function * integral of second - int differentiation of first *integral of second

Now applying this rule would result in following:

sec x * sec x - int secx tanx * sec x dx

=sec^2 x - int sec^2 x tan x dx Hint: [let tan x =t so that sec^ x dx =dt]

= sec^2 x - 1/2 tan^2 x +C