1. The problem statement, all variables and given/known data Lim(t->(inf)) 1/2((t^2)+1) + (ln|(t^2)+1|)/2 - 1/2 2. Relevant equations N/A (unless L'Hopital's rule can be counted as an equation for this section) 3. The attempt at a solution Background: The problem started with: inf ∫(x^3)/((x^2)+1)^2 dx 0 Using partial fraction decomposition, and using two separate online calculators to verify the answer, this came to: 1/2((x^2)+1) + (ln|(x^2)+1|)/2 Per requirements for bounds at infinity, I substituted infinity for t, coming out to: 1/2((t^2)+1) + (ln|(t^2)+1|)/2 - 1/2 This appears to be something to use L'hopital's rule on. It is in 0 + Infinity state at the beginning. Given the infinity involved, the 1/2 is ignored as it is numerical insignificant as t becomes maximally large. Making the appropriate simplification: (1 + ((t^2) + 1)(ln|(t^2)+1|))/((2t^2)+2) To save a bit of typing, L'hopital's rule, for the first two times, but after t dropped out of the denominator, it was reintroduced in the third derivative set, and seems to go on forever (implying the limit does not exist). When I plug in the original integral with a very large upper bound, it appears to be going to zero. However, I'm not satisfied with that; I need to know what I'm doing wrong in this limit that is causing it to give me an incorrect answer.