Evaluating The Integrator: 1/(x^2+a^2)(x^2+y^2+a^2)^(1/2)

[daudaudaudau]

Hi.


Does anyone know how The Integrator evaluated this:

http://integrals.wolfram.com/index.jsp?expr=1/((x^2+a^2)*(x^2+y^2+a^2)^(1/2))&random=false"

?

 

[arildno]

Well..perhaps along these lines:
$$k^{2}\equiv{y}^{2}+a^{2}, x=kSinh(u)\to\sqrt{x^{2}+y^{2}+a^{2}}=k\Cosh(u), dx=kCosh(u)du$$, whereby our integral should roughly be something like:
$$\int\frac{kdu}{a^2+k^{2}Sinh^{2}(u)}$$
Maybe.

 

[daudaudaudau]

bump