I'm working with a professor on a project and we are going through a bunch of integrals in the "table of integrals series and products" and there is one that we cannot seem to get--the answer in the book is wrong after doing some numerical calculations, but we can't find a "solution" to the integral...(adsbygoogle = window.adsbygoogle || []).push({});

So, here is the crazy integral...

[tex]

\int_{0}^\infty \frac{dx}{(1+x^2)^\frac{3}{2}*\sqrt(1+\frac{4x^2}{3(1+x^2)^2}+\sqrt(1+\frac{4x^2}{3(1+x^2)^2}))}

[/tex]

the answer that the book gives is

[tex]

\frac{\pi}{2\sqrt6}

[/tex]

but, like I said, this is not the value of the above integral. We are trying to determine two things--first, what the given integral equals, and second, what integral corresponds to the answer given...

a few interesting things to note that I have come across that might help someone out...

[tex]

\int_{0}^\infty \frac{dx}{(1+x^2)^\frac{3}{2}*\sqrt(1+\frac{4x^2}{3(1+x^2)^2}+\sqrt(1+\frac{4x^2}{3(1+x^2)^2}))} =

\int_{0}^\infty \frac{x}{(1+x^2)^\frac{3}{2}*\sqrt(1+\frac{4x^2}{3(1+x^2)^2}+\sqrt(1+\frac{4x^2}{3(1+x^2)^2}))}

[/tex]

also...

[tex]

\frac{\pi}{2\sqrt6} = \frac{\sqrt(\sum_{n=1}^\infty \frac{1}{n^2})}{2}

[/tex]

And, Im not sure if it will help any, but the one other thing that i've gotten is that

[tex]

\int_{0}^{1}\int_{0}^{1} \frac{3dxdy}{4(1-x^2y^2)} = \frac{\pi^2}{6}

[/tex]

any help or comments would be greatly appreciated...

cheers

~matt

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# Integral with nested roots

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