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Question
Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`
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Solution
Let I = `int sqrt(tanx)/(sin x . cosx).dx`
Dividing numerator and denominator by cos2x, we get
I = `int(((sqrttanx)/(cos^2x)))/((sinx/cosx)).dx`
= `int (sqrt(tanx).sec^2x)/tanx.dx`
= `int sec^2x/sqrt(tanx).dx`
Put tan x = t
∴ sec2xdx = dt
∴ I = `int (1)/sqrt(t)dt`
= `int t^(-1/2) dt`
= `t^(1/2)/(1/2) + c`
= `2sqrt(t) + c`
= `2sqrt(tanx) + c`.
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