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Calculus II
3. Techniques of Integration
Description
Building on our knowledge, we investigate multiple ways of integration such as algebraic substitutions; integration by parts; integration of power of trigonometric functions; trigonometric substitutions; partial fraction decomposition and using integral tables; calculators and computers. Being a challenging topic, we've included literally hundreds of solved problems to explore many different types of integrals. Since these integrals can be very difficult for many students, we've provided many problems to demonstrate the different intricacies of techniques of integration.
Sections of this topic include:
1. Algebraic Substitutions
In this first stage of Integration Techniques, we investigate various ways of using a u-substitution to change a difficult integral into a known integral. The group within this section is: integrating using algebraic substitutions.
2. Integration By Parts
This section investigates using an integration formula called Integration By Parts to investigate various integrals that may be the inverse result of the product rule. The group within this section is: Evaluating Integrals using Integration By Parts.
3. Integration of Powers of Trigonometric Functions
For future sections in this topic, we will need the skill of integrating trigonometric functions to various powers. So, we multiple ways to integrate these integrals using identities, simplification of trigonometric functions, and using previous integration strategies. The group within this section is called: Integration of Powers of Trigonometric Functions.
4. Trigonometric Substitutions
In this section, we explore using trigonometric substitutions to transform complex integrals into integrals of trigonometric functions to powers. Using our last section, we then find the results of these integrals. The group within this section is called: Integrating Using Trigonometric Substitutions.
5. Partial Fractions; Denominators Containing Linear Factors; Denominators Containing Irreducible Quadratic Factors
Applying all previous sections now to this section, we investigate how to integrate rational functions by using a method called Partial Fraction Decomposition.
6. Integral Tables, Calculators and Computers (Coming Soon)
In this final section, we explore how to integrate using either integral tables, calculators with integration capabilities, or computer integration software and websites. | 
