Question

Write \( \int \cot x \, dx \).

Hint:

For trigonometric integrals like \( \cot x \), use substitution or standard forms; \( \int \cot x \, dx = \ln |\sin x| + c \).

Answer 1

\[ \cot x = \frac{\cos x}{\sin x}. \] Use substitution: Let \( u = \sin x \), so \( du = \cos x \, dx \), and: \[ \int \cot x \, dx = \int \frac{\cos x}{\sin x} \, dx = \int \frac{1}{u} \, du = \ln |u| + c = \ln |\sin x| + c. \] Alternatively, the result can be written as: \[ \int \cot x \, dx = \ln |\sin x| + c. \]