Chapter 8 - Integration Techniques, L'Hopital's Rule, and Improper Integrals - Review Exercises - Page 579: 3

$= \frac{1}{2} \ln | x^{2} - 49| + C$

$\int \frac{x}{x^{2} - 49} $ Let $u = x^{2} - 49$ $u' = 2x$ $\frac{du}{dx} = 2x$ $\frac{du}{2} = x$ $\frac{1}{2} \int u^{-1} du$ $= \frac{1}{2} \ln |u| + C$ $= \frac{1}{2} \ln | x^{2} - 49| + C$