Worked problem in calculus. The antiderivative of tan^2(x) is computed.

1. Definition of Antiderivative
2. Antiderivative of a Polynomial
3. Antiderivative of (x-1)(x-2)/sqrt(x^3)
4. Basic Trig Antiderivatives
5. Antiderivative of tan^2(x)
6. Antiderivative of sin(x)/[1-sin^2(x)]
7. Visualizing an Antiderivative
8. Graphing f(x) from f'(x)
9. Antiderivative of a Piecewise-Defined Function
10. Solving Differential Equations
11. Equations of Motion
12. Overview of Rectangular Approximation of Area
13. Rectangular Approximation of Area
14. Overview of Summation Formulas
15. Limit Summation Formula
16. General Method for Integer Power Sum Formula
17. Riemann Sum with Signed Area
18. Limit Process for Area
19. Definition of Definite Integral
20. Definite Integral as Area 1 - Using the Graph
21. Definite Integral as Area 2 - Breaking Up the Region
22. Definite Integral as Area 3 - Area Below the x-axis
23. The First Fundamental Theorem of Calculus
24. Area Under a Curve 1
25. Area Under a Curve 2
26. The Mean Value Theorem for Integrals
27. Example of Mean Value Theorem for Integration
28. The Second Fundamental Theorem of Calculus
29. Example of 2nd Fundamental Theorem of Calculus 1
30. Example of 2nd Fundamental Theorem of Calculus 2
31. Integration By Substitution: Antiderivatives
32. Integration by Substitution: Definite Integrals
33. Example of Integration by Substitution 1: f(x) = (-x)/[(x+1)-sqrt(x+1)]
34. Example of Integration by Substitution 2: f(x) = x^5/(1-x^3)^3
35. Example of Integration by Substitution 3: f(x) = x^2(1+x)^4 over [0,1]
36. Example of Integration by Substitution 4: f(x) = (2x+3)/sqrt(2x+1)
37. Example of Integration by Substitution 5: f(x) = sin(x)/cos^3(x)
38. Example of Trapezoid Rule with Error Bound
39. Example of Simpson's Rule with Error Bound

In this second chapter of a series of calculus lessons, Dr. Bob covers integral calculus, including topics such as: Antiderivatives, Area, Definite Integrals, Fundamental Theorems of Calculus, Integration by Substitution, Trapezoid and Simpson's Rules. This series has 39 lessons, and it is a continuation of Part I: Limits and Derivatives.