Integrate the following functions w.r.t. x : tan 3x tan 2x tan x - Mathematics and Statistics

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Sum

Integrate the following functions w.r.t. x :  tan 3x tan 2x tan x

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Solution

Let I = `int tan 3x tan 2x tanx dx`
Consider tan 3x = tan (2x + x)

= `(tan2x + tanx)/(1 - tan2x tanx)`

∴ tan3x (1 – tan 2x tan x) = tan 2x + tan x
∴ tan 3x –  tan 3x tan 2x tan x = tan 2x + tan x
∴ tan 3x –  tan 2x –  tan x = tan 3x tan 2x tan x
I = `int (tan3x - tan 2x - tanx)dx`

= `int tan3xdx - int tan2x dx - int tanx dx`

= `(1)/(3)log|sec3x| - (1)/(2)log|sec2x| - log|secx| + c`.

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

APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 3 Indefinite Integration
Exercise 3.2 (A) | Q 2.13 | Page 110

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