$(1$ point$)$

Use the Integral Test to determine whether the infinite series is convergent.

${\displaystyle \underset{n=19}{\overset{}{}}}\frac{n^2}{(n^3+6{)}^{\frac{5}{2}}}$

Fill in the corresponding integrand and the value of the improper integral.

Enter inf for $,-$inf for $-,$ and DNE if the limit does not exist.

Compare with ${\displaystyle \underset{19}{\overset{}{}}}$

$dx=$

By the Integral Test, the infinite series ${\displaystyle \underset{n=19}{\overset{}{}}}\frac{n^2}{(n^3+6{)}^{\frac{5}{2}}}$

A$.$ converges

B$.$ diverges