I assume that by "apache" you mean the Apache Tomcat servlet container, since you are referring to a maven artifact which is a Java build tool.
Disclamer: I don't know what "dynatrace" is and I don't know which logging you specifically want.
But as far as the Apache Tomcat servlet container and X-Ray goes - here is the link to get started:
http://docs.aws.amazon.com/xray/latest/devguide/xray-sdk-java.html
Start by adding AWSXRayServletFilter as a servlet filter to trace incoming requests. A servlet filter creates a segment While the segment is open you can use the SDK client's methods to add information to the segment and create subsegments to trace downstream calls. The SDK also automatically records exceptions that your application throws while the segment is open.
As for the mentioned maven artifact:
aws-xray-recorder-sdk-apache-http – Instruments outbound HTTP calls made with Apache HTTP clients
So, you'll need this if, let's say, a client makes a request to your Tomcat server and your Tomcat server makes a request to another server thus acting as a client in this case.