Primitive of Reciprocal of 1 plus Cosine of a x/Corollary
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Theorem
- $\ds \int \frac {\d x} {1 + \cos x} = \tan \frac x 2 + C$
Proof
\(\ds \int \frac {\d x} {1 + \cos a x}\) | \(=\) | \(\ds \frac 1 a \tan \frac {a x} 2 + C\) | Primitive of $\dfrac 1 {1 + \cos a x}$ | |||||||||||
\(\ds \leadsto \ \ \) | \(\ds \int \frac {\d x} {1 + \cos x}\) | \(=\) | \(\ds \tan \frac x 2 + C\) | setting $a \gets 1$ |
$\blacksquare$
Sources
- 1976: K. Weltner and W.J. Weber: Mathematics for Engineers and Scientists ... (previous) ... (next): $6$. Integral Calculus: Appendix: Table of Fundamental Standard Integrals