Answer
$$3\root 3 \of x - 5{e^x} + C$$
Work Step by Step
$$\eqalign{
& \int {\left[ {{x^{ - 2/3}} - 5{e^x}} \right]} dx \cr
& {\text{sum rule}} \cr
& = \int {{x^{ - 2/3}}} dx - \int {5{e^x}} dx \cr
& = \int {{x^{ - 2/3}}} dx - 5\int {{e^x}} dx \cr
& {\text{integrate by using the power rule and }}\int {{e^x}dx} = {e^x} + C \cr
& = \frac{{{x^{ - 2/3 + 1}}}}{{ - 2/3 + 1}} - 5{e^x} + C \cr
& {\text{simplifying}} \cr
& = \frac{{{x^{1/3}}}}{{1/3}} - 5{e^x} + C \cr
& = 3{x^{1/3}} - 5{e^x} + C \cr
& = 3\root 3 \of x - 5{e^x} + C \cr} $$
