Primitive of Cosine Function/Proof 2

Theorem

$\ds \int \cos x \rd x = \sin x + C$


Proof

\(\ds \int \cos x \rd x\) \(=\) \(\ds \frac 1 2 \int \paren {e^{i x} + e^{-i x} } \rd x\) Euler's Cosine Identity
\(\ds \) \(=\) \(\ds \frac 1 {2 i} \paren {e^{i x} - e^{-i x} } + C\) Primitive of Exponential of a x
\(\ds \) \(=\) \(\ds \sin x + C\) Euler's Sine Identity

$\blacksquare$

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