Nginx virtual host config file etc/nginx/sites-available/example.com

default

server {
  listen 80 default_server;
  listen [::]:80 default_server;

  root /var/www/html;
  index index.html index.htm index.nginx-debian.html;
  server_name _;
  
  location / {
    try_files $uri $uri/ =404;
  }

  location /shiny/ {
    proxy_pass http://127.0.0.1:3838/;
    proxy_http_version 1.1;
    proxy_set_header Upgrade $http_upgrade;   
    proxy_set_header Connection "upgrade";
    rewrite ^(/shiny/[^/]+)$ $1/ permanent;
  }

  location /rstudio/ {
    proxy_pass http://127.0.0.1:8787/;
    proxy_http_version 1.1;
    proxy_set_header Upgrade $http_upgrade;
    proxy_set_header Connection "upgrade";
  }

}

example.com

server { 
  listen 80; 
  listen [::]:80;
  root /var/www/html;

  server_name example.com www.example.com;
        location / {
            proxy_pass http://127.0.0.1:3838/example/;
            proxy_http_version 1.1;
            proxy_set_header Upgrade $http_upgrade;
            proxy_set_header Connection "upgrade";
        }
}