Partial Fractions Integration
Decompose rational functions then integrate.
Key idea
Decompose rational functions then integrate.
In depth
Split a rational function into simpler fractions, which integrate to logs and arctans. Do polynomial division first if the degree of the numerator is at least that of the denominator.
Worked example
∫ 1/(x² − 1) dx = ½∫(1/(x − 1) − 1/(x + 1)) dx = ½ ln|(x − 1)/(x + 1)| + C.
Real-world uses
- Integrating rational models of drug dosage and chemical reaction rates
Common mistake
Forgetting repeated or irreducible quadratic factors need special forms.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Partial Fractions Integration?
Decompose rational functions then integrate. It is a topic at the expert level in Calculus.
Where is Partial Fractions Integration used in real life?
Real-world examples: Integrating rational models of drug dosage and chemical reaction rates.
What should I learn before Partial Fractions Integration?
Make sure you are comfortable with Trigonometric Substitution, the previous topic in Calculus.
What is a common mistake with Partial Fractions Integration?
Forgetting repeated or irreducible quadratic factors need special forms.
How can I practise Partial Fractions Integration?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Partial Fractions Integration?
Move on to Improper Integrals next.
Related expert topics in Calculus
- Derivatives of Inverse Trig – Derivatives of arcsin, arccos, arctan.
- Implicit Differentiation – Differentiate both sides of F(x,y)=0 treating y as a function of x.
- Logarithmic Differentiation – Take logs before differentiating products and powers.
- Related Rates – Link rates of change of connected quantities.
- Linear Approximation – Approximate f near a using its tangent line.
- Differentials – Use dy = f′(x)dx for small changes.