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Question
Integrate the functions:
`sqrt(tanx)/(sinxcos x)`
Solution
Let `I = int (sqrt tan x)/(sinx cos x)` dx
`= int sqrt tan x/(sin x/ cos x * cos ^2) dx`
`= int sqrt tanx/tan x * sec^2 x dx`
`I = int (tan x)^((-1)/2)* sec^2 x dx`
Put tan x = t
sec2 x dx = dt
Hence, `I = int t^((-1)/2)dt = (t ^(1/2 + 1))/(1/2 + 1) + C`
`= 2 t^(1/2) + C`
`= 2 sqrt(tan x) + C`
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