∫12x2-5 dx - Mathematics and Statistics

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Sum

`int 1/sqrt(2x^2 - 5)  "d"x`

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Solution

Let I = `int 1/sqrt(2x^2 - 5)  "d"x`

= `int  1/sqrt(2(x^2 - 5/2))  "d"x`

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

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

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

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Chapter 2.3: Indefinite Integration - Short Answers I

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