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

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"` &there4; I = `1/sqrt(2) log|x + sqrt(x^2 - 5/2)| + "c"`

∫12x2-5 dx - Mathematics and Statistics

Question

$\int \frac{1}{\sqrt{2 x^{2} - 5}} d x$

Sum

Solution

Let I = $\int \frac{1}{\sqrt{2 x^{2} - 5}} d x$

= $\int \frac{1}{\sqrt{2 (x^{2} - \frac{5}{2})}} d x$

= $\frac{1}{\sqrt{2}} \int \frac{1}{\sqrt{x^{2} - {(\frac{\sqrt{5}}{\sqrt{2}})}^{2}}} d x$

= $\frac{1}{\sqrt{2}} \log | x + \sqrt{x^{2} - {(\frac{\sqrt{5}}{\sqrt{2}})}^{2}} | + c$

∴ I = $\frac{1}{\sqrt{2}} \log | x + \sqrt{x^{2} - \frac{5}{2}} | + c$

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Methods of Integration: Integration by Parts

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Chapter 2.3: Indefinite Integration - Short Answers I

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Chapter 2.3 Indefinite Integration
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