calculus - Integration of $(5^{3/x}-sqrt[3]{x^8}+9)/(3x^2)$

Problem: evaluate $$\int\frac{5^{3/x}-\sqrt[3]{x^8}+9}{3x^2}\mathrm dx$$

Please provide me a hint. I tried to separate to 3 parts but don't know how to integrate $\frac{5^{3/x}}{3x^2}$.

Answer

Hint: Let $u = \frac{3}{x}$, and then $du = \frac{-3}{x^2} dx$. Then

$$\int \frac{5^{3/x}}{x^2} dx = \int 5^u \frac{du}{-3}$$