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Integrate the following w.r.t.x : x21-x6 - Mathematics and Statistics

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Sum

Integrate the following w.r.t.x : `x^2/sqrt(1 - x^6)`

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Solution

Let I = `int x^2/sqrt(1 - x^6)*dx`
Put x3 = t
∴ 3x2dx = dt

∴ x2dx = `(1)/(3)*dt`

∴ I = `(1)/(3) int 1/sqrt(1 - t^2)*dt`

= `(1)/(3)sin^-1 (t) + c`

= `(1)/(3)sin^-1 (x^3) + 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 3.06 | Page 150
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