You also need to use the brands.css stylesheet in font-awesome 5.0.8. Additionally, you need to make sure your class names are up to date. Try the snippet below:
<link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.0.8/css/brands.css" integrity="sha384-IiIL1/ODJBRTrDTFk/pW8j0DUI5/z9m1KYsTm/RjZTNV8RHLGZXkUDwgRRbbQ+Jh" crossorigin="anonymous">
<link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.0.8/css/fontawesome.css" integrity="sha384-q3jl8XQu1OpdLgGFvNRnPdj5VIlCvgsDQTQB6owSOHWlAurxul7f+JpUOVdAiJ5P" crossorigin="anonymous">
<i class="fab fa-btc"></i>
<i class="fab fa-bitcoin"></i>
Alternatively, you can just use the all.css stylesheet to include all the styles
<link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.0.8/css/all.cs