Help with this separable differential equation

[dmayers94]

The problem is dx/dt = (x+9)^2.
This is separable so I made it dx / (x+9)^2 = dt.
The only method I can think of using for something like this is partial fraction, but I can't get it to work with A/(x+9) + B/(x+9).
Can anyone find a method that works?

 

[Mandelbroth]

The problem is dx/dt = (x+9)^2.
This is separable so I made it dx / (x+9)^2 = dt.
The only method I can think of using for something like this is partial fraction, but I can't get it to work with A/(x+9) + B/(x+9).
Can anyone find a method that works?

FYI, the partial fraction decomposition would be $\frac{A}{(x+9)}+\frac{B}{(x+9)^2}$.

This aside, you can simply use the idea of the power rule for integration. What is the integral of 1/u², for example?