Integrate the following functions w.r.t. x : 1sinx.cosx+2cos2x - Mathematics and Statistics

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Sum

Integrate the following functions w.r.t. x : `(1)/(sinx.cosx + 2cos^2x)`

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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)/(t + 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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Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 3 Indefinite Integration
Exercise 3.2 (A) | Q 2.04 | Page 110

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