Primitive of Reciprocal of Tangent of a x

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Theorem

$\displaystyle \int \frac {\d x} {\tan a x} = \frac 1 a \ln \size {\sin a x} + C$


Proof

\(\displaystyle \int \frac {\d x} {\tan a x}\) \(=\) \(\displaystyle \int \cot a x \rd x\) Cotangent is Reciprocal of Tangent
\(\displaystyle \) \(=\) \(\displaystyle \frac 1 a \ln \size {\sin a x} + C\) Primitive of $\cot a x$

$\blacksquare$


Also see


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