SUMMARY
The integral of the function 1/(2x + 2x^2) can be solved using partial fraction decomposition rather than integration by parts. The correct factorization of the denominator is 2x(x + 1), which allows for the application of partial fractions. The final solution to the integral is -(1/2)ln(x + 1) + (1/2)ln(x). This approach clarifies the importance of recognizing the appropriate method for integration based on the structure of the function.
PREREQUISITES
- Understanding of basic integration techniques
- Familiarity with partial fraction decomposition
- Knowledge of logarithmic properties
- Ability to factor polynomials
NEXT STEPS
- Study partial fraction decomposition techniques in calculus
- Practice integrating rational functions using various methods
- Review properties of logarithms for simplification
- Explore advanced integration techniques such as integration by substitution
USEFUL FOR
Students studying calculus, particularly those focusing on integration techniques, and educators looking for examples of rational function integration methods.