Step $2$

Use the Power Rule for Integration to simplify ${\displaystyle \underset{4}{\overset{7}{}}}(\frac{2}{x^2}-1)dx={\displaystyle \underset{4}{\overset{7}{}}}\frac{2}{x^2}dx-{\displaystyle \underset{4}{\overset{7}{}}}(1)dx.$

So$,$

${\displaystyle \underset{4}{\overset{7}{}}}(\frac{2}{x^2}-1)dx={\displaystyle \underset{4}{\overset{7}{}}}\frac{2}{x^2}dx-{\displaystyle \underset{4}{\overset{7}{}}}(1)dx$

$=2[\frac{x}{-1}{]}_4^7-[x{]}_4^7$

$=-2[\frac{1}{x}{]}_4^7-[x{]}_4^7$

$=\frac{3}{14}$