Mr. Integral

THE BIG IDEA

Integration Methods

Which integration method fits this structure?

Integration has no single rule that works for every expression. Learn to spot products, trigonometric powers, radicals and rational factors, then choose a transformation that simplifies the remaining work.

Begin the first lesson →See the lesson route ↓

5 lessons · No deadlines or locked lessons

SEE THE CONNECTIONS

How the ideas fit together.

A map of the main ideas. Follow a node to its lesson.

  1. Start with01Products
  2. other integrands need02Trig structure
  3. trig identities also simplify03Radicals
  4. algebraic decomposition handles04Rational factors

YOUR LEARNING ROUTE

One idea at a time.

Read the explanation, use the visualization, then try the check before opening its reasoning.

Keep the unit cheat sheet handy →
Lessons in this unit5 lessons
  1. 01Integration by PartsChoose which factor to differentiate, carry boundary terms, and recognize a recurring integral.
  2. 02Integrating Trigonometric PowersUse parity and identities to turn trigonometric products into substitutions or simpler frequencies.
  3. 03Trigonometric Substitution and BranchesChoose a substitution that simplifies a quadratic radical and preserve the sign of its square root.
  4. 04Rational Integration and Partial FractionsDecompose a proper rational expression using the factor structure of its denominator.
  5. 05Hyperbolic Functions and Inverse IntegralsUse exponential definitions to derive hyperbolic identities and select an inverse-function antiderivative.