The image you uploaded features some integral calculus content. Here's what I can observe:

1. The first integral is $\int \frac{8x - 1}{2x^2 - 3x - 2} \, dx$.
2. There are also some calculations and steps for other problems on the board, like solving for $x = 5$ and some other algebraic steps.

Would you like me to walk you through solving this integral or explain any other part of the content in the image?

Here are some related questions to expand the topic:

1. How do you perform partial fraction decomposition on rational functions?
2. What are some common techniques for integrating rational functions like the one in the image?
3. How do you solve algebraic equations like $x^2 + x - n = 0$?
4. Can you explain how to apply the power rule for integration?
5. How can you determine the constants of integration in indefinite integrals?

Tip: Always check if partial fraction decomposition is possible when dealing with rational expressions. This can simplify the integration process significantly.