How do I know when to use integration by partial fraction?

Integration by partial fractions is a useful technique when dealing with rational functions, which are fractions where both the numerator and the denominator are polynomials. Here are some key indicators to help you determine when to use this method:

Identifying Suitable Functions

Look for these characteristics in the function you want to integrate:

• Rational Function: Ensure the integrand is a fraction with polynomials in both the numerator and denominator.
• Degree of the Numerator: The degree of the numerator must be less than the degree of the denominator. If it’s not, perform polynomial long division first.

Steps to Follow

Once you've confirmed the function meets the criteria, follow these steps:

• Factor the denominator into linear or irreducible quadratic factors.
• Set up the partial fraction decomposition based on these factors.
• Solve for the unknown coefficients in the decomposition.

When to Avoid This Method

There are situations where integration by partial fractions may not be the best choice:

• If the function is not a rational function.
• If the degree of the numerator is greater than or equal to the degree of the denominator.

By recognizing these patterns, you can effectively decide when to apply integration by partial fractions in your calculus problems.