Primitive of Secant Function
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Theorem
Secant plus Tangent Form
- $\ds \int \sec x \rd x = \ln \size {\sec x + \tan x} + C$
where $\sec x + \tan x \ne 0$.
Tangent plus Angle Form
- $\ds \int \sec x \rd x = \ln \size {\map \tan {\frac x 2 + \frac \pi 4} } + C$
Also presented as
Some sources present this result as the primitive of the reciprocal of the cosine function:
\(\ds \int \dfrac {\d x} {\cos x}\) | \(=\) | \(\ds \ln \size {\sec x + \tan x} + C\) | ||||||||||||
\(\ds \int \dfrac {\d x} {\cos x}\) | \(=\) | \(\ds \ln \size {\map \tan {\frac x 2 + \frac \pi 4} } + C\) |