\(\int \cot x \, dx = \ln|\sin x| + c\)

\(\int \sec x \, dx = \ln|\sec x + \tan x| + c = \ln\left|\tan\left(\frac{\pi}{4} + \frac{x}{2}\right)\right| + c\)

\(\int \text{cosec } x \, dx = \ln\left|\tan\frac{x}{2}\right| + c = -\ln|\text{cosec } x + \cot x| + c\)

\(\int \frac{f'(x)}{f(x)} dx = \ln|f(x)| + c\)