SUMMARY
The integral of the function \(\sqrt{e^{9x}}\) is not simply \(\int(e^{9x/2}) dx\). The correct approach requires recognizing that \(\sqrt{e^{9x}} = e^{9x/2}\) and applying the integral formula correctly. The correct integral is \(\frac{2}{9} e^{9x/2} + C\). This highlights the importance of verifying results by differentiation to ensure accuracy.
PREREQUISITES
- Understanding of integral calculus
- Familiarity with exponential functions
- Knowledge of differentiation techniques
- Basic algebraic manipulation skills
NEXT STEPS
- Study integration techniques for exponential functions
- Learn about the properties of square roots in integration
- Practice differentiation to verify integral results
- Explore common mistakes in integral calculus
USEFUL FOR
Students and educators in mathematics, particularly those focusing on calculus, as well as anyone looking to improve their skills in solving integrals involving exponential functions.