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Evaluate the following integrals : int(t...

Evaluate the following integrals : `int(tanx)/(secx+tanx)dx`

Text Solution

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We have given,
`I=int(tan x)/(sec x+tan x)dx,`
`I=int(tan x(sec x-tan x))/((sec x+tan x)(sec x-tan x))dx,`
multiplyingand dividing by `(sec x-tan x)`
`I=int(tan x sec x-tan^(2)x)/(sec^(2)x-tan^(2)x)dx,`
`I=int (tan x*sec x-tan^(2)x)/(sec^2x-tan^2x)dx`
Hence `sec^(2)x-tan^(2)x=1`
`I=int (tan x*sec x-sec^(2)x+1)dx,`
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