There might be a language problem between us. The integral is complicated, not complex. Complex means that variables are imaginary numbers. It also matters what "p" is. It appears that p must be >1/2. It would also be easier to understand if the variable of integration r were not the same as the upper bound r. Clarify these, and I will give it a try.
Hello! I'll take your integral to some mathemathician friends at the University of Buenos Aires, Argentina. I don't promise anything, but I'll see what can I do for you.