Primitive of Reciprocal of Cotangent of a x

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Theorem

$\displaystyle \int \frac {\d x} {\cot a x} = \frac {-\ln \size {\cos a x} } a + C$


Proof

\(\displaystyle \int \frac {\d x} {\cot a x}\) \(=\) \(\displaystyle \int \tan a x \rd x\) Cotangent is Reciprocal of Tangent
\(\displaystyle \) \(=\) \(\displaystyle \frac {-\ln \size {\cos a x} } a + C\) Primitive of $\tan a x$

$\blacksquare$


Also see


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