It looks like you've uploaded an image with a mathematical equation. Let me analyze and walk through the details of the expression you've shared.

The problem appears to involve a surface area integral formula. Based on the image, the equation seems to be:

$S = 2\pi \int_{1/2}^{1} \left( \frac{x^3}{4} + \frac{1}{3x} \right) \sqrt{1 + \left( \frac{3x^2}{4} - \frac{1}{3x^2} \right)^2} \, dx$

The equation simplifies in the second step to:

$S = 2\pi \int_{1/2}^{1} \left( \frac{3x^5}{16} + \boxed{\text{something}} \right) \, dx$

It looks like you're either solving for an integral involving a surface area or working with a specific formula for a solid of revolution. The boxed part suggests that you need to compute the remaining simplification.

Let me break this down for you further. Would you like me to proceed with calculating or simplifying this integral, or is there a specific part you'd like to discuss?