Integrals of Exponential Functions

Integrals of exponential functions play a pivotal role in calculus, particularly in areas like differential equations, probability theory, and physics. These integrals involve expressions of the form \( \int e^{ax} \, dx \) or \( \int e^{f(x)} \, dx \), where \( a \) is a constant and \( f(x) \) is a function. Understanding their properties and techniques for their evaluation is fundamental in solving a wide range of mathematical problems. From modeling growth and decay processes to analyzing complex systems, mastering the integration of exponential functions provides a powerful toolset for tackling diverse mathematical challenges.