To compute the integral of $e^{-t}$, we solve:

$\int e^{-t} \, dt$

Solution:

The integral of $e^{-t}$ is computed as: $\int e^{-t} \, dt = -e^{-t} + C$ where $C$ is the constant of integration.

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Would you like more details or have any questions?

Here are 5 related questions for exploration:

1. How do you find the integral of $e^{-at}$, where $a$ is a constant?
2. What is the definite integral of $e^{-t}$ from 0 to infinity?
3. How is $e^{-t}$ used in real-world applications like radioactive decay or population models?
4. How would you compute the integral of $te^{-t}$?
5. What happens when you differentiate $-e^{-t}$?

Tip: Always include the constant of integration $C$ when computing indefinite integrals!