sorry I dont know how to use latex yet im going to learn now but I need help if you can.
Integral from 0 to infinity of (x^3)/(x^2+1)^2 dx
and
Integral from 0 to 3 of (1)/(x-1)^1/3 dx
I do not think this converges because numerator is degree three and denominator is degree four. It has to be at least 2 apart in degrees. Are you asking to find its value of to tell if it converges or not. Because if you are asking the latter the answer is it does not converge.