## Calculus (3rd Edition)

$$2(\ln x)^2+5\ln x+c$$
Using the facts that $\int du/u=\ln u$ and $\int udu=u^2/2$, we have $$\int \frac{4\ln x+5}{x}dx=\int \frac{4\ln x}{x} +\frac{5}{x}dx\\ =\int 4\ln x \ d(\ln x) +\int \frac{5}{x}dx \\ =2(\ln x)^2+5\ln x+c$$