How to integrate (validate) recapcha in submit page

I'm using simple ajax commenting system and i dont now how to integrate recaptcha in submit page!

AJAX COMMENT.PHP

<?php

// Error reporting:
error_reporting(E_ALL^E_NOTICE);

include "connect.php";
include "comment.class.php";


/*
/   Select all the comments and populate the $comments array with objects
*/
$id = empty($_GET['id'])?0:$_GET['id'];
$comments = array();
$result = mysql_query("SELECT * FROM comments where url='$id' ORDER BY id desc");

while($row = mysql_fetch_assoc($result))
{
    $comments[] = new Comment($row);
}

?>



<table width="800" border="0" class="komentar" cellpadding="0" cellspacing="0">
<tr>
<td width="480">

<div id="addCommentContainer"  style="width:500px; overflow-x:hidden;">
</div>

<div id="main" style="width:500px; overflow-x:hidden;">

<?php

/*
/   Output the comments one by one:
*/

foreach($comments as $c){
    echo $c->markup();
}

?>

</div>



</td>



<td valign="top" width="320">
    <table width="300" border="0"  cellpadding="0" cellspacing="0">
    <tr>
    <td height="16"  background="commentfg.png" style="background-repeat:no-repeat;">               

    </td>
    </tr>  

    <tr>
    <td height="20"  background="commentfs.png">                
    <form id="addCommentForm" method="post" action="">
        <div style="margin-left:15px; color:white;">

            <label for="name">Vase ime:&nbsp&nbsp</label><br>
            <input type="text" name="name" id="name" />

         <p><label for="email">Email: (bice sakriven)&nbsp&nbsp</label><br>
            <input type="text" name="email" id="email" /></p>


            <input type="hidden" name="url" id="url" value="<?php $id = empty($_GET['id'])?0:$_GET['id']; echo $id;?>"/>

            <label for="body">Unesite komentar:&nbsp&nbsp</label><br>
            <textarea name="body" id="body" cols="30" rows="5" onKeyDown="limitText(this.form.body,this.form.countdown,200);" 
onKeyUp="limitText(this.form.body,this.form.countdown,200);"></textarea><br><br>
            Broj preostalih znakova:(max 200):<input readonly type="text" name="countdown" size="3" value="200"> 
<br>
  <script type="text/javascript"
     src="http://www.google.com/recaptcha/api/challenge?k=6LeQc8MSAAAAAMGe16dslbxCRu3Frs_265JhH88j">
  </script>
  <noscript>
     <iframe src="http://www.google.com/recaptcha/api/noscript?k=6LeQc8MSAAAAAMGe16dslbxCRu3Frs_265JhH88j"
         height="300" width="500" frameborder="0"></iframe><br>
     <textarea name="recaptcha_challenge_field" rows="3" cols="40">
     </textarea>
     <input type="hidden" name="recaptcha_response_field"
         value="manual_challenge">
  </noscript>
<br>

            <input type="submit" id="submit" value="Potvrdi" />

        </div>
    </form>
    </td>
    </tr>

    <tr>
    <td height="16"  background="commentfd.png" style="background-repeat:no-repeat;">               

    </td>
    </tr> 
    </table>    




</td>
</tr>
</table>
<script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.4.2/jquery.min.js"></script>
<script type="text/javascript" src="script.js"></script>

COMMENT.CLASS.php

<?php
class Comment
{
    private $data = array();

    public function __construct($row)
    {
        /*
        /   The constructor
        */

        $this->data = $row;
    }

    public function markup()
    {
        /*
        /   This method outputs the XHTML markup of the comment
        */

        // Setting up an alias, so we don't have to write $this->data every time:
        $d = &$this->data;

        $link_open = '';
        $link_close = '';



        // Converting the time to a UNIX timestamp:
        $d['dt'] = strtotime($d['dt']);

        // Needed for the default gravatar image:
        $url = 'http://'.dirname($_SERVER['SERVER_NAME'].$_SERVER["REQUEST_URI"]).'/img/default_avatar.png';

        return '
           <div  style="width:500px; overflow-x:hidden;">
            <table width="500" >
            <tr>
            <td valign="top" width="100" height="120" background="avatar.png" style="background-repeat:no-repeat;" align="center">

                <div class="avatar" style="width:100px; overflow-x:hidden; margin-top:10px; ">
                    '.$link_open.'
                    <img src="http://www.gravatar.com/avatar/'.md5($d['email']).'?size=50&amp;default='.urlencode($url).'" />
                    '.$link_close.'
                </div>
                <div style="width:80px; height:40px; overflow:hidden;">
                <font color="#47a5db">'.$link_open.$d['name'].$link_close.'</font>
                </div>

            </td>   
            <td width="400" valign="top">
                <table width="400" border="0"  cellpadding="0" cellspacing="0">
                <tr>
                <td height="开发者_如何学运维20" valign="bottom" background="commentg.png" style="background-repeat:no-repeat;">
                <div class="date" title="Added at '.date('H:i \o\n d M Y',$d['dt']).'" style="margin-left:10px;">
                <font color="silver" size="-1">'.date('d M Y',$d['dt']).'</font>
                </div>              
                </td>
                </tr>

                <tr>
                <td background="comments.png" style="background-repeat:repeat-y;">
                <div style="width:350px; overflow-x:hidden; margin-top:0px; margin-left:10px;">
                <p><font color="white"><b>'.$d['body'].'</b></font></p>
                </div>
                </td>
                </tr>

                <tr>
                <td height="20"  background="commentd.png" style="background-repeat:no-repeat;">                

                </td>
                </tr>
                </table>

            </td>
            </tr>
            </table>
          </div>    
        ';
    }

    public static function validate(&$arr)
    {
        /*
        /   This method is used to validate the data sent via AJAX.
        /
        /   It return true/false depending on whether the data is valid, and populates
        /   the $arr array passed as a paremter (notice the ampersand above) with
        /   either the valid input data, or the error messages.
        */

        $errors = array();
        $data   = array();

        // Using the filter_input function introduced in PHP 5.2.0

        if(!($data['email'] = filter_input(INPUT_POST,'email',FILTER_VALIDATE_EMAIL)))
        {
            $errors['email'] = 'Unesite validan Email!';
        }

        if(!($data['url'] = filter_input(INPUT_POST,'url',FILTER_CALLBACK,array('options'=>'Comment::validate_text'))))
        {
            // If the URL field was not populated with a valid URL,
            // act as if no URL was entered at all:

            $errors['url'] = 'Please enter a url.';
        }

        // Using the filter with a custom callback function:

        if(!($data['body'] = filter_input(INPUT_POST,'body',FILTER_CALLBACK,array('options'=>'Comment::validate_text'))))
        {
            $errors['body'] = 'Niste uneli komentar!';
        }

        if(!($data['name'] = filter_input(INPUT_POST,'name',FILTER_CALLBACK,array('options'=>'Comment::validate_text'))))
        {
            $errors['name'] = 'Niste uneli ime!';
        }

        if(!empty($errors)){

            // If there are errors, copy the $errors array to $arr:

            $arr = $errors;
            return false;
        }

        // If the data is valid, sanitize all the data and copy it to $arr:

        foreach($data as $k=>$v){
            $arr[$k] = mysql_real_escape_string($v);
        }

        // Ensure that the email is lower case:

        $arr['email'] = strtolower(trim($arr['email']));

        return true;

    }

    private static function validate_text($str)
    {
        /*
        /   This method is used internally as a FILTER_CALLBACK
        */

        if(mb_strlen($str,'utf8')<1)
            return false;

        // Encode all html special characters (<, >, ", & .. etc) and convert
        // the new line characters to <br> tags:

        $str = nl2br(htmlspecialchars($str));

        // Remove the new line characters that are left
        $str = str_replace(array(chr(10),chr(13)),'',$str);

        return $str;
    }

}

?>

SUBMIT.PHP

<?php

// Error reporting:
error_reporting(E_ALL^E_NOTICE);

include "connect.php";
include "comment.class.php";

/*
/   This array is going to be populated with either
/   the data that was sent to the script, or the
/   error messages.
/*/

$arr = array();
$validates = Comment::validate($arr);

if($validates)
{
    /* Everything is OK, insert to database: */

    mysql_query("   INSERT INTO comments(name,url,email,body)
                    VALUES (
                        '".$arr['name']."',
                        '".$arr['url']."',
                        '".$arr['email']."',
                        '".$arr['body']."'
                    )");

    $arr['dt'] = date('r',time());
    $arr['id'] = mysql_insert_id();

    /*
    /   The data in $arr is escaped for the mysql query,
    /   but we need the unescaped variables, so we apply,
    /   stripslashes to all the elements in the array:
    /*/

    $arr = array_map('stripslashes',$arr);

    $insertedComment = new Comment($arr);

    /* Outputting the markup of the just-inserted comment: */

    echo json_encode(array('status'=>1,'html'=>$insertedComment->markup()));

}
else
{
    /* Outputtng the error messages */
    echo '{"status":0,"errors":'.json_encode($arr).'}';
}

?>

Generally

1. Call captcha script on your comment (submit) page. It sets value to session variable (e.g. $_SESSION["captcha"]).
2. Put text input in your submit form to get user's answer on captcha (if it's not provided with captcha script).
3. In submit script check if session value matches user's input.