Primitive of Reciprocal of Secant of a x

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Theorem

$\displaystyle \int \frac {\d x} {\sec a x} = \frac {\sin a x} a + C$


Proof

\(\displaystyle \int \frac {\d x} {\sec a x}\) \(=\) \(\displaystyle \int \cos a x \rd x\) Secant is Reciprocal of Cosine
\(\displaystyle \) \(=\) \(\displaystyle \frac {\sin a x} a + C\) Primitive of $\cos a x$

$\blacksquare$


Also see


Sources