Evaluate the following : ∫125-9x2.dx - Mathematics and Statistics

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Sum

Evaluate the following : `int (1)/(25 - 9x^2).dx`

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Solution

I = `int (1)/(25 - 9x^2).dx`

= `int(1)/(5^2 - (3x)^2).dx`

= `(1)/(2(5))log |(5 + 3x)/(5 - 3x)|.(1)/(3) + c`

= `(1)/(30)log |(5 + 3x)/(5 - 3x)| + c`.

Alternative Method :

`int (1)/(25 - 9x^2).dx`

= `(1)/(9) int (1)/((25)/(9)x^2).dx`

= `(1)/(9) int (1)/((5/3)^2 - x^2).dx`

= `(1)/(9) xx (1)/(2 xx 5/3)log|(5/3 + x)/(5 / 3 - x)|+ c`

= `(1)/(30)log|(5 + 3x)/(5 - 3x)| + c`.

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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 1.02 | Page 123

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