These are just nuisance integrals with coefficients to obscure the problem.
You will probably just need to use trig substitutions to get them.
For the sqrt(9+25x2) you should probably try x= (3/5) tan θ and for sqrt(9-25x2) try either
x=(3/5) sin θ or (3/5) cos θ.
Then you will need to do some manipulations to get them to some recognizable form; the ones with a plus sign under the radical should come to an arctan and the ones with a minus should come to either an arcsin or arccos.