It's quite simple, on your app/Exceptions/Handler.php on top the of it add this two imports:
use Request;
use Log;
Then on your report method add this:
public function report(Exception $e) {
Log::info($e->getMessage(), [
'url' => Request::url(),
'input' => Request::all()
]);
return parent::report($e);
}
Now whenever you get an exception the current url is logged and the request parameters either GET or POST will also be logged:
[2016-02-10 19:25:13] local.INFO: Error Processing Request {"url":"http://localhost:8002/list","input":{"name":"fabio","surname":"antunes"}}