Primitive of Reciprocal of Secant of a x
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Theorem
- $\ds \int \frac {\d x} {\sec a x} = \frac {\sin a x} a + C$
Proof
\(\ds \int \frac {\d x} {\sec a x}\) | \(=\) | \(\ds \int \cos a x \rd x\) | Secant is Reciprocal of Cosine | |||||||||||
\(\ds \) | \(=\) | \(\ds \frac {\sin a x} a + C\) | Primitive of $\cos a x$ |
$\blacksquare$
Also see
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 14$: Integrals involving $\sec a x$: $14.455$