Answer
$$ - 2{x^{ - 5}} + \frac{9}{4}{x^{4/3}} + 2.5x + C$$
Work Step by Step
$$\eqalign{
& \int {\left( {\frac{{10}}{{{x^6}}} + 3\root 3 \of x + 2.5} \right)} dx \cr
& {\text{separate the integrand}} \cr
& = \int {\frac{{10}}{{{x^6}}}} dx + \int {3\root 3 \of x } dx + \int {2.5dx} \cr
& {\text{rewrite}} \cr
& = \int {10{x^{ - 6}}} dx + \int {3{x^{1/3}}} dx + \int {2.5dx} \cr
& {\text{integrate by using the power rule}} \cr
& = \frac{{10{x^{ - 5}}}}{{ - 5}} + \frac{{3{x^{4/3}}}}{{4/3}} + 2.5x + C \cr
& = - 2{x^{ - 5}} + \frac{9}{4}{x^{4/3}} + 2.5x + C \cr} $$
