## Calculus 10th Edition

$\frac{1}{2}((\ln(2e))^{2})-(\ln(2)^2)$ Or $\approx1.193$
$\int_{1}^{e}\frac{\ln(2x)}{x}dx$ Use u-subsitution. $\frac{du}{dx}= \ln(2x)$ $\frac{du}{dx}=\frac{1}{2x}(2)$ $dx=xdu$ $\int_{1}^{e}\frac{ux}{x}du$ $\int_{1}^{e}udu$ $\frac{u^{2}}{2}|_{1}^{e}$ $\frac{(\ln(2x))^{2}}{2}|_{1}^{e}$ $(\frac{(\ln(2e))^{2}}{2})-(\frac{(\ln(2))^{2}}{2})$ $\frac{1}{2}((\ln(2e))^{2})-(\ln(2)^2)$ Or $\approx1.193$