Executing <script> elements inserted with .innerHTML

I've got a script that inserts some content into an element using innerHTML.

The content could for example be:

<script type="text/javascript">alert('test');</script>
<strong>test</strong>

Problem is that the code inside the <script> tag doesn't get executed. I googled it a bit but there were no apparent solutions. If I inserted the content using jQuery $(element).append(content);the script parts got eval'd before being injected into the DOM.

Has anyone got a snippet of code that executes all the <script> elements? The jQuery code was a bit complex so I couldn't really figure out how it was done.

Edit:

By peeking into the jQuery code I've managed to figure out how jQuery does it, which resulted in the following code:

Demo:
<div id="element"></div>

<script type="text/javascript">
  function insertAndExecute(id, text)
  {
    domelement = document.getElementById(id);
    domelement.innerHTML = text;
    var scripts = [];

    ret = domelement.childNodes;
    for ( var i = 0; ret[i]; i++ ) {
      if ( scripts && nodeName( ret[i], "script" ) && (!ret[i].type || ret[i].type.toLowerCase() === "text/javascript") ) {
            scripts.push( ret[i].parentNode ? ret[i].parentNode.removeChild( ret[i] ) : ret[i] );
        }
    }

    for(script in scripts)
    {
      evalScript(scripts[script]);
    }
  }
  function nodeName( elem, name ) {
    return elem.nodeName && elem.nodeName.toUpperCase() === name.toUpperCase();
  }
  function evalScript( elem ) {
    data = ( elem.text || elem.textContent || elem.innerHTML || "" );

    var head = document.getElementsByTagName("head")[0] || document.documentElement,
    script = document.createElement("script");
    script.type = "text/javascript";
    script.appendChild( document.createTextNode( data ) );
    head.insertBefore( script, head.firstChild );
    head.removeChild( script );

    if ( elem.parentNode ) {
        elem.parentNode.removeChild( elem );
    }
  }

  insertAndExecute("element", "<scri"+"pt type='text/javascript'>document.write('This text should appear as well.')</scr"+"ipt><strong>this text should also be inserted.</strong>");
</script>

Simplified ES6 version of @joshcomley's answer with an example.

No JQuery, No library, No eval, No DOM change, Just pure Javascript.

http://plnkr.co/edit/MMegiu?p=preview

var setInnerHTML = function(elm, html) {
  elm.innerHTML = html;
  Array.from(elm.querySelectorAll("script")).forEach( oldScript => {
    const newScript = document.createElement("script");
    Array.from(oldScript.attributes)
      .forEach( attr => newScript.setAttribute(attr.name, attr.value) );
    newScript.appendChild(document.createTextNode(oldScript.innerHTML));
    oldScript.parentNode.replaceChild(newScript, oldScript);
  });
}

Usage

$0.innerHTML = HTML;    // does *NOT* run <script> tags in HTML
setInnerHTML($0, HTML); // does run <script> tags in HTML

@phidah... Here is a very interesting solution to your problem: http://24ways.org/2005/have-your-dom-and-script-it-too

So it would look like this instead:

<img src="empty.gif" onload="alert('test');this.parentNode.removeChild(this);" />

The OP's script doesn't work in IE 7. With help from SO, here's a script that does:

exec_body_scripts: function(body_el) {
  // Finds and executes scripts in a newly added element's body.
  // Needed since innerHTML does not run scripts.
  //
  // Argument body_el is an element in the dom.

  function nodeName(elem, name) {
    return elem.nodeName && elem.nodeName.toUpperCase() ===
              name.toUpperCase();
  };

  function evalScript(elem) {
    var data = (elem.text || elem.textContent || elem.innerHTML || "" ),
        head = document.getElementsByTagName("head")[0] ||
                  document.documentElement,
        script = document.createElement("script");

    script.type = "text/javascript";
    try {
      // doesn't work on ie...
      script.appendChild(document.createTextNode(data));      
    } catch(e) {
      // IE has funky script nodes
      script.text = data;
    }

    head.insertBefore(script, head.firstChild);
    head.removeChild(script);
  };

  // main section of function
  var scripts = [],
      script,
      children_nodes = body_el.childNodes,
      child,
      i;

  for (i = 0; children_nodes[i]; i++) {
    child = children_nodes[i];
    if (nodeName(child, "script" ) &&
      (!child.type || child.type.toLowerCase() === "text/javascript")) {
          scripts.push(child);
      }
  }

  for (i = 0; scripts[i]; i++) {
    script = scripts[i];
    if (script.parentNode) {script.parentNode.removeChild(script);}
    evalScript(scripts[i]);
  }
};