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Integrate the following w.r.t.x : 1(1-cos4x)(3-cot2x) - Mathematics and Statistics

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Sum

Integrate the following w.r.t.x : `(1)/((1 - cos4x)(3 - cot2x)`

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Solution

Let I = `int (1)/((1 - cos4x)(3 - cot2x))*dx`

= `int (1)/(2sin^2 2x(3 - cot2x))*dx`

= `(1)/(2) int ("cosec"^2x)/(3 - cot2x)*dx`

Put 3 – cot 2x = t
∴ 2 cosec22x·dx = dt

∴ cosec22x·dx = `(1)/(2)*dt`

∴ I = `(1)/(4) int 1/t*dt`

= `(1)/(4)log|t| + c`

= `(1)/(4)log|3 - cot2x| + c`.

Concept: Methods of Integration: Integration Using Partial Fractions
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APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 3 Indefinite Integration
Miscellaneous Exercise 3 | Q 3.07 | Page 150
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