You can add the above search widget to a Moodle page via any text editor:
Click the down arrow in the far left corner 
and then select the html editor view button: 
Copy and paste the following html:
<!-- EBSCOhost Custom Search Box Begins -->
<script src="https://widgets.ebscohost.com/eit/scripts/ebscohostsearch2.js" type="text/javascript"></script>
<style type="text/css">
.ebscohostCustomSearchBox47761 {font-family:Helvetica,Verdana,Arial,sans-serif;width:300px;}
.ebscohostCustomSearchBox47761 #databaseblock {width:98%;}
.ebscohostCustomSearchBox47761 .choose-db-list{ list-style-type:none;padding:0;margin:10px 0 0 0;font-size:9pt; width:100%;}
.ebscohostCustomSearchBox47761 .choose-db-check{ width:20px;float:left;padding-left:5px;padding-top:5px; }
.ebscohostCustomSearchBox47761 .choose-db-detail{ margin-left:30px;border-left:solid 1px #E7E7E7;padding:5px 11px 7px 11px;line-height:1.4em; }
.ebscohostCustomSearchBox47761 .summary { background-color:#1D5DA7;color:#FFFFFF;border:solid 1px #1D5DA7; }
.ebscohostCustomSearchBox47761 .two, .ebscohostCustomSearchBox47761 .one, .ebscohostCustomSearchBox47761 .selected {border:solid 1px #E7E7E7; border-top:0;}
.ebscohostCustomSearchBox47761 #disciplineBlock47761 { width:auto; }
.ebscohostCustomSearchBox47761 .limiter { float:left;margin:0;padding:0;width:50%; }
.ebscohostCustomSearchBox47761 #ebscohostsearchtext47761 { width: 144px; }
.ebscohostCustomSearchBox47761 #ebscohostsearchtext47761.edspub { width: 245px; }
.ebscohostCustomSearchBox47761 .ebscohostCustomSearchBox47761 .ebscohost-search-button.edspub {
border: 1px solid #156619;
padding: 5px 10px !important;
border-radius: 3px;
color: #fff;
font-weight: bold;
background-color: #156619;
}
.ebscohostCustomSearchBox47761 .ebscohost-title.edspub {
color: #1c7020;
font-weight: bold;
}
.visually-hidden {
border: 0;
clip: rect(0 0 0 0);
height: 1px;
overflow: hidden;
padding: 0;
position: absolute;
white-space: nowrap;
width: 1px;
}
</style>
<form class="ebscohostCustomSearchBox47761" action="" onsubmit="return ebscoHostSearchGo(this,47761);" method="post" style="overflow:hidden;">
<input id="ebscohostwindow" name="ebscohostwindow" type="hidden" value="1" />
<input id="ebscohosturl" name="ebscohosturl" type="hidden" value="https://login.proxy103.nclive.org/login?url=http://search.ebscohost.com/login.aspx?direct=true&scope=site&type=1&site=ehost-live&lang=en" />
<input id="ebscohostsearchsrc47761" name="ebscohostsearchsrc47761" type="hidden" value="db" />
<input id="ebscohostsearchmode" name="ebscohostsearchmode" type="hidden" value="+" />
<input id="ebscohostkeywords" name="ebscohostkeywords" type="hidden" value="" />
<div style="background-image:url('https://widgets.ebscohost.com/images/logos/researchdatabases.gif'); background-repeat:no-repeat; height:66px; width:300px; font-size:9pt; color:#353535;">
<div style="padding-top:5px;padding-left:75px;">
<span class="ebscohost-title " style="font-weight:bold;">Research databases</span>
<div>
<label class="visually-hidden" for="ebscohostsearchtext47761">Search Terms</label>
<input id="ebscohostsearchtext47761" class="" name="ebscohostsearchtext47761" type="text" size="23" style="font-size:9pt;padding-left:5px;margin-left:0px;" />
<input type="submit" value="Search" class="ebscohost-search-button " style="font-size:9pt;padding-left:5px;" />
</div>
</div>
</div>
<div id="limiterblock" style="margin-left:-px; overflow: auto; ">
<div id="limitertitle" style="font-weight:bold;padding-top:25px;padding-bottom:5px;">Limit Your Results</div>
<div class="limiter" >
<input type="checkbox" id="chkFullText47761" name="chkFullText47761" />
<label for="chkFullText47761">Full Text</label>
</div>
<div class="limiter" style="display:none;">
<input type="checkbox" id="chkReferencesAvailable47761" name="chkReferencesAvailable47761" />
<label for="chkReferencesAvailable47761">References Available</label>
</div>
<div class="limiter" >
<input type="checkbox" id="chkPeerReviewed47761" name="chkPeerReviewed47761" />
<label for="chkPeerReviewed47761">Peer Reviewed</label>
</div>
</div>
<div id="databaseblock" style="float:left;margin:0;padding:0;padding-left:4px;">
<ul class="choose-db-list choose-db-list-47761">
<li class="summary">
<span class="choose-db-check" title="Select / Deselect all">
<input type="checkbox" onclick="SelectAllCheckBoxes(this,47761);" name="cball47761" id="cball47761"/>
</span>
<div class="choose-db-detail">
<label for="cball47761">
<span style="font-weight:bold;color:#FFFFFF;font-size:9pt;"> Select / Deselect all</span>
</label>
</div>
</li>
<li id="tr46" class="two">
<span class="choose-db-check" title="APA PsycARTICLES">
<input type="checkbox" id="cb4647761" name="cbs47761" value="pdh" checked="checked" />
</span>
<div class="choose-db-detail">
<label for="cb4647761">
APA PsycARTICLES
</label>
</div>
</li>
<li id="tr49" class="one">
<span class="choose-db-check" title="APA PsycINFO">
<input type="checkbox" id="cb4947761" name="cbs47761" value="psyh" checked="checked" />
</span>
<div class="choose-db-detail">
<label for="cb4947761">
APA PsycINFO
</label>
</div>
</li>
</ul>
</div>
</form>
<!-- EBSCOhost Custom Search Box Ends -->