Question: On Wikipedia, it is stated that the Biot-Savart law is a formula used for determining the magnetic field pseudovector **B**(**r**) at a position vector **r** due to a current-carrying wire, but that the formula only works for constant/steady electric currents. Wikipedia then states the law:

[![enter image description here](https://i.stack.imgur.com/FqA1d.png)](https://i.stack.imgur.com/FqA1d.png)

So my question then is, if the magnetostatic assumption is employed, would it be okay to factor that current term $I$ out of the line integral? And if it is legitimate, why do most textbooks leave it in the integrand? Is there some hidden benefit to doing so?

Answer: 
As you said, "A slow draw stores energy in the bow that is then released quickly."

The speed of the string, and therefore the speed of the arrow, is much faster than the archer's arm can move. The arrow's kinetic energy is proportional to the square of its speed.

Greater speed translates to greater range.

Greater energy translates to greater penetrating power.

Note that upon impact with a target, the arrow can exert a much greater force than the bow string exerts on the arrow, because the target may decelerate the arrow much faster than the string accelerates it.
These answers are missing the point.

When you throw an arrow, most of the kinetic energy goes into your arm. When you draw it back with a bow, most of it goes to the bow and almost none goes to your arm.

A truck has way more energy than a baseball, but it's still better for a human to throw a baseball than hit it with a truck.