Integration with Partial Fractions 3 - Distinct Mixed Factors
by
Robert Donley

### Lecture Description

Worked problem in calculus. The indefinite integral of f(x) = (3x^2+2)/(x^2+1)(x^2-x) is computed using partial fractions with distinct linear/quadratic factors. Two methods are presented for obtaining constant terms.

### Course Index

- Int by Parts 1 - Natural Log and Exponential
- Int by Parts 2 - Trig Functions
- Int by Parts 3 - Definite Integrals
- Int by Parts 4 - Antiderivative of e^(2x)cos(x) (Double IBP)
- Int By Parts 5 - Antiderivative for e^{3x}cos(4x) (Fast Solution)
- Int by Parts 6 - Antiderivative of sec^3(x)
- Fast Antiderivative of x^2 exp(3x)
- Integrals with cos^m(x) sin^n(x)
- Integral of cos(mx)cos(nx)
- Integral of tan^m(x) sec^n(x)
- Antiderivative of sec^5(x)
- Integral of tan^6(x)
- Trig Substitution 1 - Basic Inverse Trig Integrals
- Trig Substitution 2 - Integral for (1+x^2)^{5/2}
- Trig Substitution 3 - Integral of x^2/sqrt(1-4x^2)
- Trig Substitution 4 - Integral of sqrt(e^{2x} - 1)
- Integration with Partial Fractions 1 - Distinct Linear Factors
- Integration with Partial Fractions 2 - Repeated Linear Factors
- Integration with Partial Fractions 3 - Distinct Mixed Factors
- Integration with Partial Fractions 4 - Repeated Quadratic Factors
- Integration with Partial Fractions 5 - Composition with e^x
- L'Hopital's Rule 1 - Rational Functions
- L'Hopital's Rule 2 - Trig Limits
- L'Hopital's Rule 3 - exp, log, and inverse sine
- L'Hopital's Rule 4 - Special Indeterminate Forms
- Growth of Functions at Infinity
- Improper Integrals 1 - Infinite Limits of Integration
- Improper Integrals 2 - Vertical Asymptote in Interval
- Improper Integral of 1/x^p
- Mean of the Exponential Distribution

### Course Description

In this series, Dr. Bob covers topics from Calculus II on the subject of advanced integration techniques, such as Integration by Parts, Trig Integrals, Trig Substitution, Partial Fraction Integrals, L'Hopital's Rule, Improper Integrals.

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