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

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Answer 1 · 2018-02-09T13:46:26

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

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#