Primitive of Reciprocal of Square of Cosine of a x
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Theorem
- $\ds \int \frac {\d x} {\cos^2 a x} = \frac {\tan a x} a + C$
Corollary
- $\ds \int \frac {\d x} {\cos^2 x} = \tan x + C$
Proof
\(\ds \int \frac {\d x} {\cos^2 a x}\) | \(=\) | \(\ds \int \sec^2 a x \rd x\) | Definition of Cosecant | |||||||||||
\(\ds \) | \(=\) | \(\ds \frac {\tan a x} a + C\) | Primitive of $\sec^2 a x$ |
$\blacksquare$
Also see
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 14$: Integrals involving $\cos a x$: $14.381$