I want to understand the steps required to compute the indefinite integral of 1/((x^2 + a^2)*Sqrt[x^2 + a^2 + b^2]).
Wolfram Mathematica gives the solution to be ArcTan[(b*x)/(a*Sqrt[a^2 + b^2 + x^2])]/(a*b)
I have tried various substitutions but cannot get anywhere near this. I can easily derive the integral of 1/(x^2+a^2) to get arctan - so Im quite proficient in doing such integrals - but I cannot find a good substitution for this one.
Any help would be greatly appreciated