Evaluate the integral. Show that the substitution $x=\sqrt[\phantom{2}]{7}sec()$ transforms I into $\frac{1}{7}{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}cos()d,$ and evaluate I in terms of $.$

$I={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{dx}{x^2\sqrt[\phantom{2}]{x^2-7}}$

$($Use symbolic notation and fractions where needed. Use $C$ for the arbitrary constant. Absorb into $C$ as much as possible.$)$

$I=$

Evaluate I in terms of $x.$

$($Use symbolic notation and fractions where needed. Use $C$ for the arbitrary constant. Absorb into $C$ as much as possible.$)$

$I=$