SUMMARY
The integral of the function \(\int_0^1 \frac{x^3 + 2ax^2}{2+x} \, dx\) can be simplified by performing polynomial long division. Dividing \(x^3 + 2ax^2\) by \(2 + x\) yields a quadratic polynomial and a remainder that can be expressed as a constant divided by \(2 + x\). This approach allows for easier integration of the resulting terms over the interval from 0 to 1.
PREREQUISITES
- Understanding of polynomial long division
- Familiarity with definite integrals
- Knowledge of integration techniques for rational functions
- Basic algebraic manipulation skills
NEXT STEPS
- Study polynomial long division in detail
- Learn techniques for integrating rational functions
- Explore the properties of definite integrals
- Practice solving integrals involving parameters
USEFUL FOR
Students studying calculus, particularly those focusing on integration techniques, as well as educators looking for examples of rational function integration.