Primitive of Reciprocal of Cosecant of a x

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Theorem

$\displaystyle \int \frac {\d x} {\csc a x} = \frac {-\cos a x} a + C$


Proof

\(\displaystyle \int \frac {\d x} {\csc a x}\) \(=\) \(\displaystyle \int \sin a x \rd x\) Cosecant is Reciprocal of Sine
\(\displaystyle \) \(=\) \(\displaystyle \frac {-\cos a x} a + C\) Primitive of $\sin a x$

$\blacksquare$


Also see


Sources