JEE Main Integration Practice Test 2025 – The Comprehensive All-in-One Guide to Mastering Your Exam!

The integral of \( e^x \) with respect to \( x \) can be determined by considering the unique property of the exponential function \( e^x \). When integrating \( e^x \), the result remains \( e^x \) itself due to the fact that the derivative of \( e^x \) is also \( e^x \).

When performing the integral, we add a constant of integration \( C \) to account for any constant value that could have been present in the original function before differentiation. Hence, the integral \( \int e^x \, dx \) is expressed as:

\[

\int e^x \, dx = e^x + C

\]

This accurately reflects the nature of exponential functions, providing a straightforward result without additional transformations or adjustments.

The other choices imply different forms or operations that do not accurately represent the integral of \( e^x \). For example, \( \ln(e)x + C \) simplifies to \( x + C \), which is not the correct result of the integration. Similarly, \( xe^x + C \) and \( e^{2x} + C \) represent different integrals, not applicable in this context.

Thus,