Hi! I need to find the limit when x-> +infinity of (integral from x to x^2 of (sqrt(t^3+1)dt))/x^5
The Attempt at a Solution
The integral of (sqrt(t^3+1)dt) can only be estimated, so sqrt(t^3+1)=(t^(3/2))*sqrt(1+1/t^3) should I use the maclaurin series first for the function sqrt(1 + 1/t^3) (but f`(0) = infinity and I also can`t use maclaurin series for sqrt(t^3+1) as t is infinity) and then take integral for the first several elements? please help, I don`t understand how should I solve this problem.
P.S. Sorry for my bad English :/