The integral of $e^{-5t} \, dt$ can be computed as follows:

$\int e^{-5t} \, dt$

This is a standard exponential integral. To solve it:

$\int e^{-5t} \, dt = \frac{e^{-5t}}{-5} + C = -\frac{1}{5} e^{-5t} + C$

Where $C$ is the constant of integration.

Final Answer:

$-\frac{1}{5} e^{-5t} + C$

Would you like further details or have any questions?

Here are 5 related questions to explore further:

1. How do you compute the integral of $e^{kt}$ for any constant $k$?
2. What is the definite integral of $e^{-5t}$ from 0 to 1?
3. How do you apply integration by substitution to exponential integrals?
4. How do you solve integrals involving products of exponentials and polynomials?
5. What is the derivative of $e^{-5t}$?

Tip:

When integrating exponentials, remember that the chain rule often applies in reverse. Look out for constants multiplied by the variable inside the exponent!