Shortcode content left with bleeding tags?

Hey everyone,

Trying to do a very simple shortcode with content:

function test_shortcode( $atts, $content = null ) {
	return '<div class="testshortcode">' . $content . '</div>';
}
add_shortcode( 'test', 'test_shortcode' );

When I use this in a post like so:

“[test]this is some text

and some more on a new line[/test]”

The output contains bleeding <p> tags:

<div class="entry-content">
		<div class="test_shortcode">this is some text</p>
<p>and some more on a new line</div>
	</div><!-- .entry-content -->

Note the bleeding </p> and <p> tags. I am using the default twentyfifteen theme with no other plugins or modifications of any kind.

I have Google’d for hours and found a tonne of differing opinions on wpautop, but I can’t seem to find a conclusive answer. Can anyone shed some light on this issue?