While in the Intro to Partial Fractions video we largely focused on decomposing rational functions whose denominators were products of non-repeating linear terms, in this video we investigate what happens if the factors are either repeating or irreducible quadratics (i.e. they can not be factored into the product of two linear terms using real numbers).
This might make the algebra more complicated, but it is effectively the same process as before: hypothesize a decomposition with undetermined coefficients, break up the equation into a system of equations you can solve, and then integrate the result. The final integrals are doable, but can sometimes take a bit of work (a u-sub or identifying the derivative of arctan(x) ).
****************************************************
YOUR TURN! Learning math requires more than just watching videos, so make sure you reflect, ask questions, and do lots of practice problems!
****************************************************
►Full Course Playlist: CALCULUS II: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n
****************************************************
Other Course Playlists:
►CALCULUS I: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m
►DISCRETE MATH: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS
►LINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6
***************************************************
► Want to learn math effectively? Check out my "Learning Math" Series:
https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw
►Want some cool math? Check out my "Cool Math" Series:
https://www.youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho
*****************************************************
►Check out my 2nd Channel for lower production quality "live" math videos: https://www.youtube.com/channel/UCFNL8G1CZ4dH0p-Jf7UXqdQ
*****************************************************
►Follow me on Twitter: http://twitter.com/treforbazett
*****************************************************
This video was created by Dr. Trefor Bazett, an Assistant Professor, Educator at the University of Cincinnati. #calculus #math
BECOME A MEMBER:
►Join: https://www.youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/join
MATH BOOKS & MERCH I LOVE:
► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett