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