I'm trying to use the integral test but I have a little problem. I don't know if I am allowed to use l'hopital's rule in integrals because having ln(n)/n^3 would give me 1/3n^3 after applying l'hopital's rule and I can show that 1/n^3 is convergent using the integral test and the comparison test as well however I have a feeling that I am not allowed to use l'hopital's rule in this case, so...what do I do?

Any input would be greatly appreciated!

Thanks in advance!