It looks like you're working with a differential equation or mathematical expression, but the notation appears to be incomplete or unclear. Could you clarify the expression so I can assist you better? Here are some potential clarifications:

1. Are you looking to solve a differential equation? If so, is there an equation relating $\frac{dv}{dt}$ or another variable?
2. Should the infinity symbol (∞) be part of the limits of integration or another concept?
3. Is there a function or equation involving $v^2 + 8v - 9$ that you would like to differentiate or solve?

Once I have a clearer understanding, I can provide a detailed solution.

If you'd like to clarify, feel free! Here are some related questions:

1. Are you trying to solve for $v$ in $v^2 + 8v - 9 = 0$?
2. Do you want to integrate or differentiate $v^2 + 8v - 9$?
3. Is ∞ meant to represent an upper limit for an integral?
4. Is this an ordinary differential equation (ODE)?
5. Would you like to evaluate an expression at infinity?

Tip: When working with differential equations, make sure to specify if the equation is ordinary or partial, as the methods differ significantly.