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Question
Integrate the following functions w.r.t. x : `(1)/(sinx.cosx + 2cos^2x)`
Solution
Let I = `int (1)/(sinx.cosx + 2cos^2x).dx`
Dividing numerator and denominator of cos2x, we get
I = `int ((1/cos^2x))/(sinx/cosx + 2).dx`
= `int sec^2x/(tan x + 2).dx`
Put tan x = t
∴ sec2x dx = dt
∴ I = `int (1)/(t + 2)dt`
= log |t + 2| + c
= log|tan x + 2| + c.
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