Question

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

Answer 1

`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`