Integrating AngularJS and RequireJS shouldn't be complicated, and it isn't with angularAMD. To see it in action, checkout this website that show case key features. Make sure to load your favorite Developer Tools to see the on-demand loading of *.js files as you switch tabs.

A quick AngularJS + RequireJS how-to using angularAMD:

Step 1:

Define components and dependencies in main.js: 
require.config({
    baseUrl: "js",    
    paths: {
        'angular': '.../angular.min',
        'angular-route': '.../angular-route.min',
        'angularAMD': '.../angularAMD.min'
    },
    shim: { 'angularAMD': ['angular'], 'angular-route': ['angular'] },
    deps: ['app']
});
and load RequireJS, and only RequireJS, in index.html: 
<head>
    <script data-main="js/main.js" src=".../require.js"></script>
</head>

Step 2:

Create app.js using RequireJS's define statement: 
define(['angularAMD', 'angular-route'], function (angularAMD) {
    var app = angular.module("webapp", ['ngRoute']);
    app.config(function ($routeProvider) {
        $routeProvider.when("/home", angularAMD.route({
            templateUrl: 'views/home.html', controller: 'HomeCtrl',
            controllerUrl: 'ctrl/home'
        }))
    });
    return angularAMD.bootstrap(app);
});

Step 3:

Create controller using app.register method: 
define(['app'], function (app) {
    app.controller('HomeCtrl', function ($scope) {
        $scope.message = "Message from HomeCtrl"; 
    });
});

Check out this Gist for a simple implementation. Then, head over to github for detail documentation.