How is hiv able to make drug resistant proteins to avert drugs that inhibit viral proteins such as reverse transcriptase, protease, or integrase? In other words, do these enzymes change their structure or not be able to be recognized by the drugs?

Through the normal process of viral replication the virus makes mistakes at a fairly predictable rate. Some of these mistakes, by chance, may be associated with a survival advantage for the virus in which it exists. This new virus will thus have a chance to produce more virus progeny (or replicate to produce more new virus particles) than other viruses. If this mutation or change in the virus happens to be associated with an increased ability to replicate in a patient who is taking a particular antiretroviral drug, this may result in an enhanced ability for viral replication in a treated patient (another way of saying the virus is drug resistant). The entire process is really one of chance which will not generally result in the outgrowth of drug resistant virus unless the patient is taking antiretroviral drugs (otherwise the survival of the resistant form does not generally have an advantage over the non-resistant form of the virus). Hope this helps.