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प्रश्न
Integrate the following functions w.r.t. x:
`(1)/(sinx.cosx + 2cos^2x)`
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उत्तर
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)/(tan + 2)dt`
= log |t + 2| + C
= log |tan x + 2| + C
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