Question: Find the constants $$a_0, a_1, a_2$$ in the asympotic expansion
$$\int_0^x t\sqrt{ln(t)} dt$$ = $a_0(x^2)(lnx)^\frac 12$ + $a_1\frac {x^2}{(lnx)^\frac 12}$ + $a_2\frac {x^2}{(lnx)^\frac 32}$ + ...
In what regime is this a useful asymptotic expansion? Justify your answer.
I'm confused about this last part, what does "In what regime" mean. Someone please help! Thank you!!