Integration By Partial Fractions

[@TheOrganicChemistryTutor]

Integration - Free Formula Sheet: bit.ly/3XCT6oz Full 2 Hour Video on Patreon: www.patreon.com/MathScienceTutor Direct Link to The Full Video: bit.ly/3zvYRG3

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9:40 Ln antiderivative examples & answer explanation, 11:17 relevant log properties, 20:18 how multiplicity affects rational function decomposition, etc. I am SO happy to find examples of problems that involve using a different method of solving for A & B without using algebraic elimination or algebraic substitution (especially for problems with more than just 2 variables like the one at 24:31). Awesome explanation & video!

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[@georgesadler7830]

Professor Organic Chemistry Tutor, thank you for another incredible video/lecture on Integration by Partial Fractions. Partial Fraction Integration is a big part of Techniques of Integration in Calculus Two. This topic is not difficult however, the algebra can get really messy from start to finish. There are multiple ways to find the constants for problems that involve Partial Fractions in Precalculus/Calculus. This is an error free video/lecture on KZbin TV with the Organic Chemistry Tutor.

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What other teachers don't seem to make us understand, you put it into a flowing liquid and make us drink it with ease. I have never understood integration by partial fraction like this before.

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docs.google.com/document/d/15xkx77jWOq3Bv6JDzrRzMNKaH5a7l5N2AMHP_QLBBq4/edit?usp=sharing

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I have a question: how do you know when to use U substitution, integration by parts, or partial fraction method when looking at an integral? What do you need to look out for in an integral to determine the method of solution? Basically what is a rule of thumb for these things?

[@314shorts]

Usually, you should try a u substitution as the first method. If that doesn’t work, then use integration by parts for multiplication or partial fractions for division. Eventually, you’ll be able to intuitively tell what integrals to use which techniques on, but it takes practice. I usually just do a u substitution in my head and then sus out whether the u substitution will take care of the entirety of the integral.

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As a general rule of thumb, I always start with u substitution. In case it didn't work, I remind myself of several procedures based on the first glance at the problem: if it contains a lone natural log, exponential function (especially e^x) or inverse trig function, I would try By Parts first. if it contains powers of sec and tan, or sin and cos, I would try Identities method first. if it contains sqrt(u^2 +- a^2), I would try Trigonometric Substitution. if it has polynomials (long expression), I would try Partial Fraction.

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