Dave4Math / Courses / Techniques of Integration

Techniques of Integration

Master techniques of integration. In this course, you'll learn integration by parts, integrating trigonometric and rational functions, and improper integrals.


January 11, 2021

Created by Dave

This course begins Summer 2021.
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Are you lost in your calculus 2 class? Can’t seem to catch up? Introducing Dave’s online math course: Techniques of Integration. Amazingly Dave teaches the lessons so that students who have never taken calculus before can understand it. Expect more from your instructor!

Who This Course is For

  • Students in college who want to learn more mathematics.
  • Anyone interested in techniques of integration.
  • Students who are enrolled in calculus 2 and want to improve their grade.
  • Anyone interested in getting prepared for calculus 3.
  • Anyone wanting to learn about integration by parts, trigonometric integrals, trigonometric substitution, integrating using partial fractions, and improper integrals.


There is no required textbook, though you will need an up-to-date web browser, paper, and pen. A hand-held scientific calculator of your choice is required.

What You’ll Learn in Techniques of Integration

  • The Method of Integration by Parts
  • Reduction Formulas
  • Integrals Involving Products of Sines and Cosines
  • Integrals Involving Products of Tangents and Secants
  • Integrals with Products of Cotan and Cosec
  • Converting to Sines and Cosines
  • Different Angles
  • Using Trigonometric Substitution
  • More Examples
  • Partial Fractions
  • Case 1: Distinct Linear Factors
  • Case 2: Repeated Linear Factors
  • Case 3: Distinct Irreducible Quadratic Factors
  • Infinite Intervals of Integration
  • Improper Integrals with Infinite Limits of Integration
  • Improper Integrals with Infinite Discontinuities
  • Improper Integrals Whose Integrands Have Infinite Discontinuities
  • A Comparison Test for Improper Integrals

Course Description

After studying the integral from calculus 1 and having seen some integral applications in calculus 2, we are now ready for an in-depth look at integration techniques. We begin this course with one of the most commonly used techniques, integration by parts. In the first lesson, we derive the formula and work through several examples of using it and when to use it.

In the next lesson, we cover trigonometric integrals. These are integrals that involve the product of trigonometric functions. In particular, the product of powers of sines and powers of cosines are detailed. Guidelines for several other forms are also detailed.

After understanding trigonometric integrals, we can now look for those integral substitutions that yield a trigonometric integral. We classify several types of substitutions here in this lesson and demonstrate how to use each one.

The method of partial fractions is explored next. We break this technique down into four cases: namely, distinct linear factors, repeated linear factors, distinct irreducible quadratic factors, and repeated irreducible quadratic factors. Each case is thoroughly discussed.

After partial fractions, we study improper integrals. We examine both infinite intervals of integration and improper integrals with infinite discontinuities. We end this fun course with a comparison test for improper integrals.

Recommended Prerequisites for Techniques of Integration

I recommend the prerequisite course Applications of the Integral. If you’re not sure if this course is for you, checkout the course contents below or find out more by checking out my free calculus 2 articles.

Course Content

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David A. Smith

Mathematics Educator

I sincerely believe that the potential in every student can be unlocked. As an accomplished and dedicated instructor, I have firm confidence that I can provide significant value to your studies.

I relish teaching and use it as a channel for my creativity as I seek to deliver real-life and relevant connections between the mathematics that I teach and my students. Promoting an active learning environment and excitement about mathematics is my dream come true.

David Smith (Dave) has a B.S. and M.S. in Mathematics and has enjoyed teaching precalculus, calculus, linear algebra, and number theory at both the junior college and university levels for over 20 years. David is the founder and CEO of Dave4Math.