Answer
$\frac{5}{2}x^{2}-\frac{1}{6x^{4}}+C$
Work Step by Step
$\int [5x+\frac{2}{3x^{5}}]dx= \int 5xdx + \int \frac{2}{3x^{5}}dx$
=$ 5\int x dx + \frac{2}{3}\int x^{-5}dx$
= $(5\times\frac{x^{2}}{2})+ (\frac{2}{3}\times\frac{x^{-4}}{-4})$+C
=$\frac{5}{2}x^{2}-\frac{1}{6x^{4}}+C$
