How Would I Isolate and Amplify a Viral Enzyme?
Each virus would contain extremely low amounts of enzyme (probably a few individual molecules, at best); collecting and concentrating enough viruses to extract a significant amount of enzyme would be long and difficult, if at all possible. 

The usual strategy in research laboratories is to clone the nucleic acid sequence coding for this protein (either by direct amplification from an HIV-infected cell, or by synthesizing a piece of DNA in vitro) and integrate it in an expression vector, that is, a larger piece of DNA, usually circular, suitable for integration in a host cell (human, or even bacterial) and carrying the sequences necessary for persistence and gene expression. This way you can produce thousands of copies of the enzyme you are interested in in each cell, and you can then purify a significant amount of integrase to study it. 

To make purification easier, it is common practice to add to the gene a sequence coding for a "purification tag", that is, a few extra amino acids that have special properties that make the final protein easier to purify. Stretches of 6-8 histidine residues are very commonly used. The assumption is that the protein carrying this tag will have an activity similar to the natural enzyme, after purification.