The image you provided shows a mathematical expression under an integral, which looks like it represents a physical scenario, possibly from electrostatics. Here's the breakdown of the expression:

$\int_{r_1}^{r_2} \frac{k_e \sigma 2\pi r d}{(r^2 + d^2)^{3/2}} \, dr$

Where:

• $k_e$ is likely the Coulomb constant (electrostatic constant).
• $\sigma$ could represent a surface charge density.
• $r$ represents the radial distance variable of integration.
• $d$ is a constant that might represent a fixed distance in the system (such as the separation between two charges or some reference point).
• $2\pi r$ comes from the geometry of the system, possibly involving a circular or cylindrical symmetry.
• The term $(r^2 + d^2)^{3/2}$ is a standard form that appears in problems involving distances in three-dimensional space.

This type of integral often arises in the calculation of electric fields due to continuous charge distributions, particularly when dealing with ring or disk geometries.

Would you like me to solve or further analyze this integral?

Here are some related questions:

1. What does $d$ represent in this problem, and does it correspond to a physical distance?
2. Is there a specific geometry (e.g., ring, disk) you're working with in this problem?
3. Are there known values for $r_1$ and $r_2$, or should they be treated as general limits?
4. Does the problem involve computing an electric field or a potential?
5. What is the physical context in which this integral appears (e.g., Gauss's law, Coulomb's law)?

Tip: When dealing with integrals that involve geometric charge distributions, it's helpful to carefully consider the symmetry of the problem to simplify the computations.