Rewrite the standard_N_q functionality

[edejong-caltech]

Purpose

Replaces quadgk with analytical integrals where possible.

To-do

Content

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• [x] I have read and checked the items on the review checklist.

[codecov[bot]]

Codecov Report

Attention: Patch coverage is 96.96970% with 1 lines in your changes are missing coverage. Please review.

Project coverage is 97.60%. Comparing base (29b59bb) to head (de913a7). Report is 17 commits behind head on main.

Files	Patch %	Lines
src/ParticleDistributions/ParticleDistributions.jl	96.96%	1 Missing :warning:

Additional details and impacted files

```diff @@ Coverage Diff @@ ## main #169 +/- ## ========================================== - Coverage 98.17% 97.60% -0.58% ========================================== Files 8 9 +1 Lines 493 500 +7 ========================================== + Hits 484 488 +4 - Misses 9 12 +3 ```

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