Primitive of Cosecant of a x
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Theorem
Tangent Form
- $\ds \int \csc a x \rd x = \frac 1 a \ln \size {\tan \frac {a x} 2} + C$
where $\tan \dfrac {a x} 2 \ne 0$.
Cosecant minus Cotangent Form
- $\ds \int \csc a x \rd x = \frac 1 a \ln \size {\csc a x - \cot a x} + C$
where $\csc a x - \cot a x \ne 0$.
Cosecant plus Cotangent Form
- $\ds \int \csc a x \rd x = -\frac 1 a \ln \size {\csc a x + \cot a x} + C$
where $\csc a x + \cot a x \ne 0$.