Primitive of Tangent of a x/Secant Form
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Theorem
- $\ds \int \tan a x \rd x = \frac {\ln \size {\sec a x} } a + C$
Proof
\(\ds \int \tan x \rd x\) | \(=\) | \(\ds \ln \size {\sec x}\) | Primitive of $\tan x$: Secant Form | |||||||||||
\(\ds \leadsto \ \ \) | \(\ds \int \tan a x \rd x\) | \(=\) | \(\ds \frac 1 a \paren {\ln \size {\sec a x} } + C\) | Primitive of Function of Constant Multiple | ||||||||||
\(\ds \) | \(=\) | \(\ds \frac {\ln \size {\sec a x} } a + C\) | simplifying |
$\blacksquare$
Also see
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 14$: Integrals involving $\tan a x$: $14.429$