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Question
Evaluate the following integrals : `int sinx/(1 + sinx)dx`
Solution
`int sinx/(1 + sinx)dx`
= `int sinx/(1 + sinx) xx (1 - sinx)/(1 - sinx)dx`
= `int(sinx - sin^2x)/(1 - sin^2x)dx`
= `int (sinx - sin^2x)/cos^2x dx`
= `int(sinx/cos^2x - sin^2x/cos^2x)dx`
= `int(1/cosx)(sinx/cosx)dx - int tan^2x dx`
= `int sec x tan x dx - int (sec^2x - 1)dx`
= `int sec x tan x dx - int sec^2x dx + int 1 dx`
= sec x – tan x + x + c.
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