Primitive of Reciprocal of Square of Cosine of a x

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Theorem

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


Proof

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

$\blacksquare$


Also see


Sources