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Route::get('ajaxrequest', 'HomeController@ajaxRequest');
Route::post('ajaxrequest', 'HomeController@ajaxRequestPost');


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<?php

namespace App\Http\Controllers;

use Illuminate\Http\Request;

class HomeController extends Controller
{
    public function ajaxRequest() {
        return view('ajaxRequest');
    }

    public function ajaxRequestPost(Request $req) {
        $input = $req->all();
        return response()->json(['success'=>'Got Simple Ajax Request.']);
    }
}


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<!DOCTYPE html>
<html>
<head>
    <title>Laravel 5.8 Ajax Request example</title>
    <meta charset="utf-8">
    <meta http-equiv="X-UA-Compatible" content="IE=edge">
    <meta name="viewport" content="width=device-width, initial-scale=1">

    <link href="//netdna.bootstrapcdn.com/bootstrap/3.2.0/css/bootstrap.min.css" rel="stylesheet">
    <script src = "https://ajax.googleapis.com/ajax/libs/jquery/2.1.3/jquery.min.js"></script>
    <meta name="csrf-token" content="{{ csrf_token() }}" />
</head>
<body>
    <div class="container">
        <h1>Laravel 5.8 Ajax Request example</h1>
        <form >
            <div class="form-group">
                <label>Name:</label>
                <input type="text" name="name" class="form-control" placeholder="Name" required="">
            </div>
            <div class="form-group">
                <label>Password:</label>
                <input type="password" name="password" class="form-control" placeholder="Password" required="">
            </div>
            <div class="form-group">
                <strong>Email:</strong>
                <input type="email" name="email" class="form-control" placeholder="Email" required="">
            </div>
            <div class="form-group">
                <button class="btn btn-success btn-submit">Submit</button>
            </div>
        </form>
    </div>

</body>
<script type="text/javascript">
    $.ajaxSetup({
        headers: {
            'X-CSRF-TOKEN': $('meta[name="csrf-token"]').attr('content')
        }
    });

    $(".btn-submit").click(function(e){
        e.preventDefault();
        var name = $("input[name=name]").val();
        var password = $("input[name=password]").val();
        var email = $("input[name=email]").val();
        $.ajax({
           type:'POST',
           url:'/ajaxrequest',
           data:{name:name, password:password, email:email},
           success:function(data){
              alert(data.success);
           }
        });
	});

</script>


</html>