Integrate the following functions w.r.t. x : xn-11+4xn - Mathematics and Statistics

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Sum

Integrate the following functions w.r.t. x : `(x^n - 1)/sqrt(1 + 4x^n)`

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Solution

Let I = `int(x^n - 1)/sqrt(1 + 4x^n).dx`

Put xn = t
∴ nxn–1 dx = dt

∴ xn–1 dx = `dt/n`

∴ I = `int (1)/sqrt(1 + 4t).dt/n`

= `(1)/nint(1 + 4t)^(-1/2)dt`

= `1/n.((1 + 4t)^(1/2))/(1/2) xx (1)/(4) + c`

= `(1)/(2n).sqrt(1 + 4x^n) + 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 1.18 | Page 110

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