Primitive of Reciprocal of Cosecant of a x

Theorem

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

Proof

\(\ds \int \frac {\d x} {\csc a x}\)

\(=\)

\(\ds \int \sin a x \rd x\)

Cosecant is Reciprocal of Sine

\(\ds \)

\(=\)

\(\ds \frac {-\cos a x} a + C\)

Primitive of $\sin a x$

$\blacksquare$

Also see

• Primitive of $\dfrac 1 {\sin a x}$

• Primitive of $\dfrac 1 {\cos a x}$

• Primitive of $\dfrac 1 {\tan a x}$

• Primitive of $\dfrac 1 {\cot a x}$

• Primitive of $\dfrac 1 {\sec a x}$

Sources

• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 14$: Integrals involving $\csc a x$: $14.465$