The US Copyright Office website confirms that the author of a work owns the copyright by virtue of being the author, except in the case of a work for hire. In that case, the person or compnay that hired the author owns the copyright. However, the way one establishes copyright ownership is by registering a claim. No other way is as good for two very important reasons.

First, until you have registered your claim, no one is under any legal obligation to pay you a licensing fee or royalties.

Second, registering your claim is prima facie evidence that you are the legitimate copyright owner. If anyone wants to contest your claim, she or he has the burden of proof

Those are two darn good reasons to pony up the $45, or $35 if you do it on-line.