The integral shown in the image appears to be of the form:

$\int e^{-x} \, dx$

To solve this integral:

1. Recognize that the integral of $e^{-x}$ is a standard integral. The result is:

$\int e^{-x} \, dx = -e^{-x} + C$

where $C$ is the constant of integration.

If there are any specific limits of integration or additional terms involved, please clarify, and I will compute accordingly.

Do you have further questions or need explanations about this integral? Here are some related problems to explore:

1. What is the integral of $e^{x}$ compared to $e^{-x}$?
2. How does the substitution method apply to integrals of the form $e^{ax}$?
3. What are the real-world applications of integrating exponential functions?
4. How do definite integrals of $e^{-x}$ differ from indefinite ones?
5. What happens if we multiply $e^{-x}$ by another function before integrating?

Tip: Always check whether an exponential integral involves coefficients or limits for more precision.