Integration of Rational Functions into Logarithms By Substitution & Long Division

This calculus video tutorial focuses on the integration of rational functions that yield logarithmic functions such as natural logs. The techniques involve include integrating by substitution, long division, and splitting a fraction into multiple smaller fractions all of which will produce natural logarithms containing absolute value functions. This video contains plenty of examples and practice problems with u-substitution of indefinite integrals & Antiderivatives generating natural log functions.

Arc Length Problems:

Surface Area Problems:

Work Problems - Calculus:

Integration By Parts:

Tabular Method:

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Trigonometric Integrals:

Trigonometric Substitution:

Integration By Partial Fractions:

Trapezoidal Rule:

Simpson's Rule:

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Improper Integrals:

Integration Into Inverse Trig:

Integration of Rational Functions:

Integral of Logarithmic Functions:

Integrating Exponential Functions:

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Calculus Final Exam and Video Playlists:

Full-Length Videos and Worksheets:

Integration - Formula Sheet:

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4:20 regular (a X and 1/a X with use of natural log) (appears in case denominator is larger and numerator is not), 6:05 regular ln (in case numerator does have exponent because that variable with exponent can't be denominator the second the denominator), 7:06 separation individually (appears in case numerator is larger and denominator is not), 9:33 factoring, 10:35 long division, u is perhaps larger one (when applying log keep in account what is give in numerator is the derivative of denominator)

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Professor Organic Chemistry Tutor, thank you for another fantastic video/lecture on Integration of Rational Functions into Logarithms by Substitutions and Long Division Methods in Calculus Two. The examples in this video shows how to recognize and integrate different types of Rational Functions in Calculus. This is an error free video/lecture on YouTube TV with the Organic Chemistry Tutor.

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