Let's consider this integration

 Integrate[
 E^(4 n x s) (1 - x)^(-1 + 4 n \[Mu]) x^(-1 + 4 n \[Nu]), {x, 0, 1}]

It returns `Gamma[4 n \[Mu]] Gamma[4 n \[Nu]] Hypergeometric1F1Regularized[
 4 n \[Nu], 4 n (\[Mu] + \[Nu]), 4 n s]`

Now let's replace those letter by numbers

 n = 20000;
 s = 0.01;
 \[Mu] = 10^-3;
 \[Nu] = 10^-3;

And let's run both the result of the integral and the integral itself

 In[28]:= Integrate[
 E^(4 n x s) (1 - x)^(-1 + 4 n \[Mu]) x^(-1 + 4 n \[Nu]), {x, 0, 1}]
 
 Out[28]= -1.786676093655969*10^352
 
 In[29]:= Gamma[4 n \[Mu]] Gamma[
 4 n \[Nu]] Hypergeometric1F1Regularized[4 n \[Nu], 
 4 n (\[Mu] + \[Nu]), 4 n s]
 
 Out[29]= 5.20048*10^228

The results differ. While I agree both look like big numbers, one is 124 orders of magnitude higher than the other one.

**Given that all calculations were analytic (no numerical approximations) we should find the same results. What causes these different results? Is this difference caused by round-off errors? How can I solve such issues?**