The expression in the image is $4e^{3x}$.

To integrate this function with respect to $x$, we need to perform the following steps:

$\int 4e^{3x} \, dx$

We can use the fact that the integral of $e^{ax}$ with respect to $x$ is $\frac{1}{a} e^{ax}$, where $a$ is a constant. Here, $a = 3$.

$\int 4e^{3x} \, dx = 4 \int e^{3x} \, dx$

Using the integral formula:

$\int e^{3x} \, dx = \frac{1}{3} e^{3x}$

Thus,

$4 \int e^{3x} \, dx = 4 \cdot \frac{1}{3} e^{3x} = \frac{4}{3} e^{3x}$

So, the integral is:

$\int 4e^{3x} \, dx = \frac{4}{3} e^{3x} + C$

where $C$ is the constant of integration.

Would you like any more details or have any questions about this integration?

Here are some related questions you might want to ask:

1. How do you integrate functions with exponential terms?
2. What is the general formula for the integral of $e^{ax}$?
3. Can you explain the concept of the constant of integration?
4. How do you integrate polynomial functions?
5. What are the basic rules of integration?

Tip: Always remember to include the constant of integration $C$ when performing indefinite integrals.