Integration by parts:

Tabular integration:
The way to get the mother functions by integration by parts.

Indeterminate Form:
If functions and are continuous at but the limit cannot be evaluated by substituting

L’Hopital’s Rule:
Suppose that and exists, and that then

Integrals with infinite integrands:
Let be a continuous function on the interval which is unbounded as then
is called an improper integral with infinite integrand at b.

Advanced integration techniques are introduced in this tutorial with the help of examples and integration methods. Tables of basic integration techniques are introduced with example problems. Strategies to calculate complicated integrals are given to show the integration by parts idea.

The rationale behind integration by parts is shown to present tabular integration. Different types of integrals involving sines and cosines are shown in some of the example problems. The products of sines and cosines are given with different types of scenarios. Trigonometric substitutions are given to calculate integrals involving trigonometric functions.

Specific Tutorial Features:

• Several example problems with step by step illustrations of solutions.
  
• Tables and graphs shown the different types of integration scenarios and important formulas.

Series Features:

• Concept map showing inter-connections of new concepts in this tutorial and those previously introduced.
  
• Definition slides introduce terms as they are needed.
  
• Visual representation of concepts
  
• Animated examples—worked out step by step
  
• A concise summary is given at the conclusion of the tutorial.

Basic formulas and integration methods
  Basic integration rules (I)
  Basic integration rules (II)
Integration by parts
  Tabular integration
  Products of sines and cosines
Trigonometric substitutions
Partial fractions and rational functions
Using integral tables and reduction formulas
Indeterminate forms and L’Hopital’s Rule
Improper Integrals