Primitive of Secant Function/Tangent plus Angle Form/Proof
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Theorem
- $\ds \int \sec x \rd x = \ln \size {\map \tan {\frac x 2 + \frac \pi 4} } + C$
Proof
\(\ds \int \sec x \rd x\) | \(=\) | \(\ds \ln \size {\tan x + \sec x} + C\) | Primitive of $\sec x$: Secant plus Tangent Form | |||||||||||
\(\ds \) | \(=\) | \(\ds \ln \size {\map \tan {\frac x 2 + \frac \pi 4} } + C\) | Tangent of Half Angle plus $\dfrac \pi 4$ |
$\blacksquare$
Sources
- 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text {II}$. Calculus: Integration: Useful substitutions: Example $2$.