To compute the integral of $e^{4x} \, dx$:

Solution

The integral of $e^{ax} \, dx$ is: $\int e^{ax} \, dx = \frac{1}{a} e^{ax} + C$ where $a$ is a constant and $C$ is the constant of integration.

Here, $a = 4$. So, $\int e^{4x} \, dx = \frac{1}{4} e^{4x} + C$

Final Answer:

$\int e^{4x} \, dx = \frac{1}{4} e^{4x} + C$

Would you like a more detailed explanation or help with similar integrals?

Related Questions:

1. How would you integrate $e^{4x^2}$?
2. What is the integral of $e^{4x} \cdot x$?
3. How does the constant $a$ affect the integral of $e^{ax}$?
4. What is the derivative of $\frac{1}{4} e^{4x}$?
5. Can you evaluate $\int_0^1 e^{4x} \, dx$ as a definite integral?

Tip: Remember, when integrating $e^{ax}$, always divide by the coefficient of $x$.