How to use a mapbox map in cartodb

I tried to integrate this map: https://a.tiles.mapbox.com/v4/felixmichel.kh7h21lp/page.html?access_token=pk.eyJ1IjoiZmVsaXhtaWNoZWwiLCJhIjoiZWZrazRjOCJ9.62fkOEqGMxFxJZPJuo2iIQ#11/47.6732/7.5352 into cartodb. But, it doesn't work. I work with cartodb.js because I added some more queries, so I needed the right link for this part:

L.tileLayer('https://a.tiles.mapbox.com/v4/felixmichel.kh7h21lp/page.html?access_token=pk.eyJ1IjoiZmVsaXhtaWNoZWwiLCJhIjoiZWZrazRjOCJ9.62fkOEqGMxFxJZPJuo2iIQ#11/47.6732/7.5352', {
      attribution: 'CartoDB'
    }).addTo(map);

Or if somebody knows a beautiful terrain map I am happy too.

Solution

Your tileLayer url is faulty, it expects the url to have placeholders for zoomlevel {z} and {x} and {y} for the axis values. You've used the url from an actual tile, which will not work.

L.tileLayer('https://a.tiles.mapbox.com/v4/felixmichel.kh7h21lp/{z}/{x}/{y}.png?access_token={token}', {
    attribution: 'Mapbox',
    subdomains: ['a','b','c','d'],
    token: 'pk.eyJ1IjoiZmVsaXhtaWNoZWwiLCJhIjoiZWZrazRjOCJ9.62fkOEqGMxFxJZPJuo2iIQ'
}).addTo(map);

Note that as you can see, it also supports the {s} placeholder to load from multiple subdomains (which must be supported by your tileprovider. Mapbox does) which is much faster because browsers can simultaneously load from four subdomains at once. I also separated the access token from the url with the {token} placeholder to demonstrate that you can use your own custom tokens if needed.

Here's a working example of this on Plunker: http://plnkr.co/edit/lsTO9KzPMyzEKr06It1I?p=preview

And here's the reference for Leaflet's L.TileLayer: http://leafletjs.com/reference.html#tilelayer