Evaluate the integral

${\displaystyle \underset{6}{\overset{}{}}}\frac{dx}{\sqrt[\phantom{2}]{x-5}}$

$($Express numbers in exact form. Use symbolic notation and fractions where needed. Use the symbol $$ for infinity.$)$

${\displaystyle \underset{6}{\overset{}{}}}\frac{dx}{\sqrt[\phantom{2}]{x-5}}=$

$$

Determine whether the series ${\displaystyle \underset{n=6}{\overset{}{}}}\frac{1}{\sqrt[\phantom{2}]{n-5}}$ converges by the Integral Test.

The series converges by the Integral Test.

The Integral Test cannot be used.

The series diverges by the Integral Test.