Because your are integrating with respect to the variable p, as that variable is changing not a, thats the way I see it
This problem is very drawn out for me, I will find out how to do it though! It will be good for both of us, but our methods seem to complicate thing while integrating and simplifying as I told by my professor, mathematicians aim to make hard things very simple when working out a problem, so we will get it! I am sure there a few around here that this is easy for, I was close to the solution but made a careless everyone and wound up with a few missing parts, like the numerator coming to p^2 instead of p^3
Lets see if we can make sense of things together, first we know -3a is a constant so we can pull that to the outside and that the numerator when integrated as if it was just alone as such becomes and remember we pulled out the -3a so now the the integrated form we get we get so somehow we need to make a relation to the denominator and decide the right method of integrating to where we can relate to this
Edit: have you tried integration by parts, I feel I am close using this method
If thec0o0lest didn't give us the answer , i won't think of this substitution .
I observed that the integral is algebraic function , not transcendental ( usually ) .
so i attempt to change the variable ( algebraic ) . It is just a trial !
Another case we can use this sub. is