Lobachevsky's integral formula and a nice application.

We present a proof of Lobachevsky's integral formula and apply it to calculate two integrals: sin(x)/x and abs(sin x)sin(x)/x. Our method involves using a Fourier expansion. Playlist:    • Interesting Integrals   Please Subscribe: https://www.youtube.com/michaelpennma... Personal Website: http://www.michael-penn.net Randolph College Math: http://www.randolphcollege.edu/mathem... Research Gate profile: https://www.researchgate.net/profile/... Google Scholar profile: https://scholar.google.com/citations?... Books I like: Abstract Algebra: Judson(online): http://abstract.ups.edu/ Judson(print): https://amzn.to/2Xg92wD Dummit and Foote: https://amzn.to/2zYOrok Gallian: https://amzn.to/2zg4YEo Artin: https://amzn.to/2LQ8l7C Differential Forms: Bachman: https://amzn.to/2z9wljH Number Theory: Crisman(online): http://math.gordon.edu/ntic/ Strayer: https://amzn.to/3bXwLah Andrews: https://amzn.to/2zWlOZ0 Calculus: OpenStax(online): https://openstax.org/subjects/math OpenStax Vol 1: https://amzn.to/2zlreN8 OpenStax Vol 2: https://amzn.to/2TtwoxH OpenStax Vol 3: https://amzn.to/3bPJ3Bn