MathProblemsBank

2.6.1.6 Fourier integral

Problem: Let \( f(x)=e^{-|x|} \cos \omega x \). Calculate the integral: \[ F(y)=\frac{1}{\sqrt{2 \pi}} \int_{-\infty}^{+\infty} f(x) e^{i y x} d x \text {. } \]