How many days has it been since the Cambrian explosion? I want to know how to calculate the number of days since an event in Earth's past, and am using the Cambrian explosion as an example.

I define a day to be one rotation of Earth with respect to the sun. The key point is that Earth's rotation has been slowing down over millions of years, so it will not be as simple as multiplying the time in years by 365.

Is there a formula for the number of days x years ago that I can simply integrate to find the answer? Or some other way to approximate?
As a very rough approximation, one could start with equation (9) from Arbab (2009), https://arxiv.org/abs/physics/0304093 to get the effective number of days per year:

$$T_{\text{eff.}} = T_0 \left(\frac{t_0-t}{t_0} \right)^{-2.6}$$

with 


$t$ the time difference between now and then
$T_0 = 365.25$ the current number of days per year 
$t_0=(13.799 \pm 0.021) \cdot 10^9$ the present age of the universe (from Planck Collaboration et al. (2015), https://arxiv.org/abs/1502.01589 )




Assuming the Cambrian explosion happened about $t_c =(541 \pm 0.13) \cdot 10^6$ years ago (from Bowring et al. (2007), https://core.ac.uk/download/pdf/62875.pdf), then the number of days since can be approximated as

$$n = \int\limits_0^{t_c} T_0 \left(1 - \frac{t}{t_0} \right)^{-2.6} \mathrm{d}t  = \left[0.625 \cdot T_0 t_0 \left(1-\frac{t}{t_0}\right)^{-\frac{8}{5}} \right]_0^{t_c} \approx 2.1 \cdot 10^{11}$$

(of course one has to keep in mind that the error on this value is rather large, but to have some ballpark figure it should be good enough)

For comparison $t_c \cdot 365.25 = 1.98 \cdot 10^{11}$