ReCaptcha is a Fuel package that handles calling reCAPTCHA.
To get captcha html:
$captcha_html = ReCaptcha::instance()->get_html();
To validate user entry:
if (ReCaptcha::instance()->check_answer(Input::real_ip(), Input::post('recaptcha_challenge_field'), Input::post('recaptcha_response_field')))
{
// valid
}
else
{
// invalid
}