Chapter 5 - Section 5.5 - The Substitution Rule - 5.5 Exercises - Page 419: 13

$$\int\frac{dx}{5-3x}=-\frac{1}{3}\ln|5-3x|+C$$

$$A=\int\frac{dx}{5-3x}$$ Let $u=5-3x$ Then $du=-3dx$. So $dx=-\frac{1}{3}du$ Substitute into $A$, we have $$A=-\frac{1}{3}\int\frac{1}{u}du$$ $$A=-\frac{1}{3}\ln|u|+C$$ $$A=-\frac{1}{3}\ln|5-3x|+C$$