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.

1. Int by Parts 1 - Natural Log and Exponential
2. Int by Parts 2 - Trig Functions
3. Int by Parts 3 - Definite Integrals
4. Int by Parts 4 - Antiderivative of e^(2x)cos(x) (Double IBP)
5. Int By Parts 5 - Antiderivative for e^{3x}cos(4x) (Fast Solution)
6. Int by Parts 6 - Antiderivative of sec^3(x)
7. Fast Antiderivative of x^2 exp(3x)
8. Integrals with cos^m(x) sin^n(x)
9. Integral of cos(mx)cos(nx)
10. Integral of tan^m(x) sec^n(x)
11. Antiderivative of sec^5(x)
12. Integral of tan^6(x)
13. Trig Substitution 1 - Basic Inverse Trig Integrals
14. Trig Substitution 2 - Integral for (1+x^2)^{5/2}
15. Trig Substitution 3 - Integral of x^2/sqrt(1-4x^2)
16. Trig Substitution 4 - Integral of sqrt(e^{2x} - 1)
17. Integration with Partial Fractions 1 - Distinct Linear Factors
18. Integration with Partial Fractions 2 - Repeated Linear Factors
19. Integration with Partial Fractions 3 - Distinct Mixed Factors
20. Integration with Partial Fractions 4 - Repeated Quadratic Factors
21. Integration with Partial Fractions 5 - Composition with e^x
22. L'Hopital's Rule 1 - Rational Functions
23. L'Hopital's Rule 2 - Trig Limits
24. L'Hopital's Rule 3 - exp, log, and inverse sine
25. L'Hopital's Rule 4 - Special Indeterminate Forms
26. Growth of Functions at Infinity
27. Improper Integrals 1 - Infinite Limits of Integration
28. Improper Integrals 2 - Vertical Asymptote in Interval
29. Improper Integral of 1/x^p
30. Mean of the Exponential Distribution

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.