Help with unsolved indefinite integral ! $\int \!r\ln \left( r \right) \sqrt {ar+{b}^{2}+{r}^{2}}\,{\rm d}r$ I really need to solve this indefinite integral: 
$\int \!r\ln  \left( r \right) \sqrt {ar+{b}^{2}+{r}^{2}}\,{\rm d}r$
It seems much more complicated than it looks. I have found a integral table with
a integral resembles my integral, and the solution involves Polylogs. The link of the intgral table is below:
http://www-elsa.physik.uni-bonn.de/~dieckman/IntegralsIndefinite/IndefInt.html
Anyone willing to take this challenge and help with this integral ? 
Thank you very much in advance 

Solution by derivative of AppellF1 function (using Mathematica):
solution = Limit[D[Integrate[r*r^t*Sqrt[a r + b^2 + r^2], r], t], t -> 0]

(* (r^2*Sqrt[b^2 + r*(a + r)]*(AppellF1[2, -1/2, -1/2, 3, (-2*r)/(a + Sqrt[a^2 - 
4*b^2]), 
 (2*r)/(-a + Sqrt[a^2 - 4*b^2])]*(-1 + 2*Log[r]) + 
2*(Derivative[0, 0, 0, 1, 0, 0][AppellF1][2, -1/2, -1/2, 3, (-2*r)/(a + Sqrt[a^2 - 
4*b^2]), 
  (2*r)/(-a + Sqrt[a^2 - 4*b^2])] + Derivative[1, 0, 0, 0, 0, 0][AppellF1][2, -1/2, 
-1/2, 3, 
  (-2*r)/(a + Sqrt[a^2 - 4*b^2]), (2*r)/(-a + Sqrt[a^2 - 4*b^2])])))/
 (4*Sqrt[(-a + Sqrt[a^2 - 4*b^2] - 2*r)/(-a + Sqrt[a^2 - 4*b^2])]*
 Sqrt[(a + Sqrt[a^2 - 4*b^2] + 2*r)/(a + Sqrt[a^2 - 4*b^2])])*)

Check:
 N[(solution /. r -> 2 /. a -> 1 /. b -> 1) - (solution /. r -> 1 /. a -> 1 /. b -> 1), 20]
 (* 1.4951478165944420424 + 0.*10^-20 I *)

 NIntegrate[r *Log[r]*Sqrt[a r + b^2 + r^2] /. a -> 1 /. b -> 1, {r, 1, 2}, WorkingPrecision -> 20]

 (* 1.4951478165944420424  *)

