Answer
$$\frac{{179}}{2}$$
Work Step by Step
$$\eqalign{
& \int_1^8 {\left( {5{x^{2/3}} - 4{x^{ - 2}}} \right)} dx \cr
& {\text{find the antiderivative by the power rule}} \cr
& = \left( {5\left( {\frac{{{x^{5/3}}}}{{5/3}}} \right) - 4\left( {\frac{{{x^{ - 1}}}}{{ - 1}}} \right)} \right)_1^8 \cr
& = \left( {3{x^{5/3}} + 4{x^{ - 1}}} \right)_1^8 \cr
& = \left( {3{x^{5/3}} + \frac{4}{x}} \right)_1^8 \cr
& {\text{part 1 of fundamental theorem of calculus}} \cr
& = \left( {3{{\left( 8 \right)}^{5/3}} + \frac{4}{8}} \right) - \left( {3{{\left( 1 \right)}^{5/3}} + \frac{4}{1}} \right) \cr
& {\text{simplify}} \cr
& = \left( {\frac{{193}}{2}} \right) - \left( 7 \right) \cr
& = \frac{{179}}{2} \cr} $$
