Primitive of Cosecant of a x

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 $\csc a x + \cot a x \ne 0$.

Also see

• Primitive of $\sin a x$
• Primitive of $\cos a x$
• Primitive of $\tan a x$
• Primitive of $\cot a x$
• Primitive of $\sec a x$