Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.2 Exercises - Page 334: 5

$\frac{1}{2}$$\ln| 2x+5|$ + C

$\int\frac{1}{2x+5} dx $ Let $u = 2x+5$ $\frac{du}{dx}$ = 2 $\frac{du}{2}$ = $dx$ Substitute $u$ and $dx$ into the original equation $\int\frac{1}{u}\frac{du}{2}$ = $\int\frac{1}{2}\frac{1}{u} du$ = $\frac{1}{2}$$\int\frac{1}{u} du$ = $\frac{1}{2}$$\ln|u|$ + C Since $u = 2x+5$, substituting it back will give you $\frac{1}{2}$$\ln| 2x+5|$ + C