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