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Integrate the following functions w.r.t. x: 1/(sin⁡𝑥.cos⁡𝑥+2⁢cos2⁡𝑥)

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Question

Integrate the following functions w.r.t. x: 

`(1)/(sinx.cosx + 2cos^2x)`

Sum
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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)/(tan + 2)dt`

= log |t + 2| + C

= log |tan x + 2| + C

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Chapter 3: Indefinite Integration - Exercise 3.2 (A) [Page 110]

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