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Question
Evaluate the following integrals : `int tanx/(sec x + tan x)dx`
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Solution
`int tanx/(sec x + tan x)dx`
= `int tanx/(sec x + tan x) xx (secx - tanx)/(sec - tan x)dx`
= `int(sec x tan x - tan^2x)/(sec^2x - tan^2x)dx`
= `int(se c tan x - (sec^2x - 1))/(1)dx`
= `int sec x tan x dx - int sec^2 x dx + int 1 dx`
= sec x – tan x + x + c.
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