Primitive of Reciprocal of Square of Cosine of a x

From ProofWiki
Jump to navigation Jump to search

Theorem

$\displaystyle \int \frac {\mathrm d x} {\cos^2 a x} = \frac {\tan a x} a + C$


Proof

\(\displaystyle \int \frac {\mathrm d x} {\cos^2 a x}\) \(=\) \(\displaystyle \int \sec^2 a x \ \mathrm d x\) Definition of Cosecant
\(\displaystyle \) \(=\) \(\displaystyle \frac {\tan a x} a + C\) Primitive of $\sec^2 a x$

$\blacksquare$


Also see


Sources