integral of 1/(x^2+1) but you didn't learn it this way in calculus 2 скачать в хорошем качестве

integral of 1/(x^2+1) but you didn't learn it this way in calculus 2

Learn more complex numbers by visiting Brilliant 👉 https://brilliant.org/blackpenredpen/ (20% off with this link!) 🛍 Euler's Identity e^(iπ)+1=0 t-shirt: https://amzn.to/427Seae When you want to use complex numbers to integrate 1/(x^2+1)! We didn't use partial fraction decomposition with complex numbers to integrate 1/(x^2+1) in calculus 2. We usually use a trigonometric substitution to integrate 1/(1+x^2), i.e. the tangent substitution. But here the key is to simplify the complex logarithms and get their principal branch. Be sure to look at the polar form of the complex numbers. Then we can integrate 1/(1+x^2) and get arctan(x), just as expected! This is definitely a great challenge question for any calculus student! ---------------------------------------- **Thanks to ALL my lovely patrons for supporting my channel and believing in what I do** AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff Julian Moik Hiu Fung Lam Ronald Bryant Jan Řehák Robert Toltowicz Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L ---------------------------------------- 💪 If you would also like to support this channel and have your name in the video description, then you could become my patron here   / blackpenredpen