Explain Why $\int\frac{f'(x)}{f(x)}\,\mathrm dx = \ln|f(x)|+C$ Explain why
$$\int\frac{f'(x)}{f(x)}\,\mathrm dx = \ln|f(x)|+C.$$

Thanks!

By the Chain rule
$$
\frac{\mathrm d}{\mathrm d x}\big(\ln|f(x)|+C\big)=\frac{1}{f(x)}\cdot\frac{\mathrm d}{\mathrm dx}f(x)=\frac{f'(x)}{f(x)}
$$
