SUMMARY
The integral of the function 4xe^(4x) is correctly calculated as xe^(4x) - 1/4e^(4x) + c. The user initially presented the integral as 4[1/4xe^(4x) - 1/16e^(4x) + c], which simplifies to the correct form. Verification through differentiation confirms the accuracy of the solution. This discussion highlights the importance of checking integration results through differentiation.
PREREQUISITES
- Understanding of integration techniques, specifically integration by parts.
- Familiarity with exponential functions and their properties.
- Knowledge of differentiation to verify integration results.
- Basic algebraic manipulation skills for simplifying expressions.
NEXT STEPS
- Study the method of integration by parts in detail.
- Practice integrating functions involving exponential terms.
- Learn how to verify integrals through differentiation.
- Explore advanced integration techniques for complex functions.
USEFUL FOR
Students and educators in calculus, mathematicians, and anyone seeking to improve their skills in integration and verification methods.