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

$\frac{1}{2}$$\ln| 2x+5| + C #### Work Step by Step \int\frac{1}{2x+5} dx Let u = 2x+5 \frac{du}{dx} = 2 \frac{du}{2} = dx Substitute u and dx into the original equation \int\frac{1}{u}\frac{du}{2} = \int\frac{1}{2}\frac{1}{u} du = \frac{1}{2}$$\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

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