Calc problem

Howdy yall

I just started calc 2 after not taking calc for about 3 years.  I was given a problem that for the life of me I couldn't figure out.  I used wolfram for the answer but I would appreciate it if someone could help me figure out how to do this problem.

http://integrals.wolfram.com/index.jsp?expr=%28a%2Bbx^2%29%2FSqrt[3ax%2Bba^3]&random=false

I know how to do most integration, but this one just blew me over.

Thanks in advance.

I only took Calc 1; and that was 16 years ago. I'll track this just to see if I understand the answer people give. I don't know quite what it would mean to have a plain square root symbol in the denominator without a number with it. But I don't remember or understand the way calc problems are written anyway. I'll stay tuned and see what people say. 

I took too long to post/already a poster ahead of me. I'll take a look and see if I can understand it.

thanks, i missed the show steps button

I think Timotheous' confusion was caused by a linking problem in the post #1: the square root does have some stuff in it, which was given in post #2.

Yes, that is correct. Thank you Elroch.

I assume you use a trigonometric substitution (let x=sqrt.(a/b) tan y, with dx=sqrt.(a/b) sec^2 y, so that the integrand eventually turns into some constant, which you can pull outside the integral symbol, times the secant cubed?  And the secant cubed is then done by parts--I'm sure you can find it. 

If it was done differently, please tell me.