Primitive of Secant of a x/Secant plus Tangent Form
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Theorem
- $\ds \int \sec a x \rd x = \frac 1 a \ln \size {\sec a x + \tan a x} + C$
where $\sec a x + \tan a x \ne 0$.
Proof
\(\ds \int \sec x \rd x\) | \(=\) | \(\ds \ln \size {\sec x + \tan x}\) | Primitive of $\sec x$: Secant plus Tangent Form | |||||||||||
\(\ds \leadsto \ \ \) | \(\ds \int \sec a x \rd x\) | \(=\) | \(\ds \frac 1 a \ln \size {\sec a x + \tan a x} + C\) | Primitive of Function of Constant Multiple |
$\blacksquare$
Also see
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 14$: Integrals involving $\sec a x$: $14.451$
- 1968: George B. Thomas, Jr.: Calculus and Analytic Geometry (4th ed.) ... (previous) ... (next): Back endpapers: A Brief Table of Integrals: $88$.