Evaluate: ∫dx/9x^2 - 25 - Mathematics and Statistics

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Sum

Evaluate: `int "dx"/("9x"^2 - 25)`

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Solution

Let I = `int "dx"/("9x"^2 - 25)`

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

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

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

∴ I = `1/30 log |(3"x" - 5)/("3x" + 5)|` + c

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Chapter 5: Integration - Miscellaneous Exercise 5 [Page 138]

APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 5 Integration
Miscellaneous Exercise 5 | Q 4.3 | Page 138

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