allery$\int \cot x\,dx$ equals
A$\log|\operatorname{cosec} x|+C$
B$\log|\cos x|+C$
C$-\log|\sin x|+C$
D$\log|\sin x|+C$
Answer & Solution
Correct answer: D. $\log|\sin x|+C$
1. Write $\cot x=\dfrac{\cos x}{\sin x}$.
2. Put $t=\sin x$, $dt=\cos x\,dx$.
3. Integral $=\int \dfrac{dt}{t}=\log|t|=\log|\sin x|+C$.
_Source: syllabus Mathematics Ch 7 "Integrals", p.300_
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