\int Cos(x) = Sin(x)

\int \frac{e^{ix} + e^{-ix}}{2} =  Cos(x)

\int \frac{e^{ix}}{2} + \int \frac{e^{-ix}}{2}

\frac{e^{ix}}{2*i}  –  \frac{e^{-ix}}{2*i}

\frac{e^{ix} – e^{-ix}}{2*i} = Sin(x)