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Evaluate: ∫dx4x2-5 - Mathematics and Statistics

Sum

Evaluate: `int "dx"/sqrt(4"x"^2 - 5)`

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Solution

Let I = `int "dx"/sqrt(4"x"^2 - 5)`

`= int 1/(sqrt (4("x"^2 - 5/4)))`dx

`= 1/2 int 1/(sqrt("x"^2 - ((sqrt5)/2)^2))` dx

`= 1/2 log |"x" + sqrt("x"^2 - (sqrt5/2)^2)|` + c

∴ I = `1/2 log |"x" + sqrt("x"^2 - 5/4)|` + c

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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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