Answer
$\int(9x+15x^{-2})dx=\frac{9}{2}x^2-\frac{15}{x}+C$
Work Step by Step
Antidifferentiating: $\int(9x+15x^{-2})dx =9\times\frac{1}{2}x^2 +15 \times\frac{1}{-1}x^{-1} + C = \frac{9}{2}x^2 - \frac{15}{x} + C$
Checking with differentiation:
$(\frac{9}{2}x^2-\frac{15}{x}+C)' = \frac{9}{2} \times2 x-15 \times\frac{-1}{x^2}= 9x + \frac{15}{x^2}$
