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!

Discover how to solve the integral of e^(-5t) with this step-by-step solution. This problem involves key calculus concepts, including exponential functions and integration rules. Suitable for college-level students or those in AP Calculus.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation