CLEP Calculus

CLEP Calculus offers students the opportunity to demonstrate their understanding of calculus concepts and applications, enabling them to earn college credit.

Advanced Topics

Techniques of Integration

Smart Ways to Integrate

Some functions are easy to integrate, but others need clever tricks!

Common Techniques

  • Substitution: Change variables to make the integral easier.
  • Integration by Parts: Useful when integrating a product of two functions.
  • Partial Fractions: Break complicated fractions into simpler pieces.

Choosing a Method

Look at the integral and decide if substitution will simplify it, or if it matches an integration by parts pattern.

Practice Makes Perfect

These techniques are like tools in a toolbox—the more you use them, the better you get!

Examples

  • To integrate \( \int x e^x , dx \), use integration by parts.

  • Rewrite \( \int \frac{1}{x^2 + x} , dx \) using partial fractions.

In a Nutshell

Special techniques help solve tricky integrals that basic rules can’t handle.