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.
When an archer pulls back on a bow, it is the bow that bends. The energy that is able to be stored and released depends a lot on by the elasticity and tensile strength of the bow, and also the size of the bow, as that determines how much advantage you can get from leverage.

Leverage I would say is one of the main issues here.

Due to the length of the string, the archer has leverage over the ends of the bow, and is able to convert more of their own strength into the tensile material and therefore the propulsion of the arrow than they would by just throwing the arrow.

I'm not sure how to word it right, but I think there is also something to do around the concept that more strength can be used when there is more resistance/potential for inertia. Consider how it is easier to throw a palm-sized rock further than a small pebble, or a javelin further than an arrow

![enter image description here](https://i.stack.imgur.com/4wDFt.gif)

<https://science.howstuffworks.com/crossbow2.htm>