COOL Dirichlet Integral 😎 @drpeyam

Uploaded December 2022 | Updated September 2026, 1 week ago

COOL Dirichlet Integral. I calculate the integral of sin(x)/x from 0 to infinity using Feynman's technique and a cool and unexpected geometric series that involves differentiation and integration. Lots of multiples of pi involved. Related to the Fresnel integral. This method doesn't use any complex analysis and is suitable for any calculus student or anyone who loves math. Big thanks to Ian Fowler for recommending this technique, he's the person who inspired me to do the anti-Pythagorean theorem video.

Anti-Pythagorean Theorem: youtu.be/TMR1oYkCKEs

YT channel: youtube.com/drpeyam
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$Laplace and ODE the fruit of our work: Laplace and ODE We use our knowledge of Laplace transforms to finally solve some ODE. You do this by applying the laplace transform and then using our Laplace miracle to get an algebra equation and then using partial fractions from calculus to find the inverse Laplace transform. Voila, no guessing involved, this gives you a really elegant way of solving differential equations, enjoy! Subscribe to my channel: https://youtube.com/drpeyam Instagram: https://www.instagram.com/peyamstagram/ Teespring merch: https://dr-peyam.creator-spring.com/?$

$life changing partial fractions trick$

$what is the plastic ratio? what is the plastic ratio? I define the plastic number and explain its properties, first as a cubic equation and a Fibonacci sequence to count bunnies, then as a fractal cube root with self similarities, and finally a cool formula with hyperbolic cosine function substitution. This is a cool journey through algebra, polynomials, inverse functions, and calculus. Proof that I did it before mathologer: https://youtu.be/SMeNVyJjd2o 0:00 Introduction 0:36 Fibonacci 1:45 Fractal 3:10 Hyperbolic trig Calculating hyperbolic trig functions: https://youtu.be/My2S-xbLPG0 YT channel: https://youtube.com/drpeyam TikTok channel: https://www.tiktok.com/@drpeyam Instagram: https://www.instagram.com/peyamstagram/ Twitter: https://twitter.com/drpeyam Teespring merch: https://teespring.com/stores/dr-peyam$ $solving a fractional differential equation$