Evaluate the following : ∫13x2-8.dx - Mathematics and Statistics

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Sum

Evaluate the following : `int (1)/sqrt(3x^2 - 8).dx`

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Solution

`int (1)/sqrt(3x^2 + 8).dx`

= `(1)/sqrt(3) int (1)/sqrt(x^2 + 8/3).dx`

= `(1)/sqrt(3) int (1)/sqrt(x^2 + (sqrt(8/3))^2).dx`

= `(1)/sqrt(3) log |x + sqrt(x^2 + (sqrt(8/3))^2)| + c_1`

= `(1)/sqrt(3) log |x + sqrt(x^2 + 8/3)| + c_1`

= `(1)/sqrt(3) log |(sqrt(3)x + sqrt(3x^2 + 8))/sqrt(3)| + c_1`

= `(1)/sqrt(3) log |sqrt(3)x + sqrt(3x^2 + 8)|  - logsqrt(3) + c_1`

= `(1)/sqrt(3) log |sqrt(3)x + sqrt(3x^2 + 8)| + c, "where"  c = c_1 - logsqrt(3)`

Alternative Method :

`int (1)/sqrt(3x^2 + 8).dx`

= `int (1)/sqrt((sqrt(3)x)^2 + (sqrt(8))^2).dx`

= `(log|sqrt(3)x + sqrt((sqrt(3)x)^2 + sqrt((8))^2| + c))/sqrt(3)`

= `(1)/sqrt(3) log |sqrt(3)x + sqrt(3x^2 + 8)| + c`.

  Is there an error in this question or solution?
Chapter 3: Indefinite Integration - Exercise 3.2 (B) [Page 123]

APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 3 Indefinite Integration
Exercise 3.2 (B) | Q 1.04 | Page 123

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