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Question
`int secx/(secx - tanx)dx` equals ______.
Options
sec x – tan x + c
sec x + tan x + c
tan x + sec x + c
– (sec x + tan x) + c
Solution
`int secx/(secx - tanx)dx` equals tan x + sec x + c.
Explanation:
`int secx/(secx - tanx)dx = int (1/cosx)/(1/cosx - sinx/cosx)dx`
= `int dx/(1 - sin x)`
= `int 1/(1 - sinx) xx (1 + sin x)/(1 + sin x)dx`
= `int (1 + sinx)/(cos^2x)dx`
= `int sec^2 x dx + int tan x sec x dx`
= tan x + sec x + c.
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