The image contains the integral expression:

$\int e^{2x} \sin(4x) \, dx$

To solve this integral, we can use the method of integration by parts or the method of repeated integration by parts since this involves both an exponential and a trigonometric function. The key is to apply the integration by parts formula:

$\int u \, dv = uv - \int v \, du$

Let me break down the process for you.

Would you like to see a detailed step-by-step solution for this integral, or would you prefer a general explanation of the technique?