2002 Chevy Impala with @ 231,000 miles has started shaking when I accelerate. on 2002 Chevrolet Impala

Shakes extensively when accelerating between 25 & 50 mph, but also at other speeds. Sometimes it shakes so much it feels like a flat tire. Also, shakes when using the accelerator or cruise control to maintain speed. Recently noticed a loud clunking noise, which usually seems like it is coming from the rear of the car. Shaking just started. The loud clunking started @ 2 weeks ago, and occurs everytime I drive, but not continuously. Gas mileage has decreased

Asked by for the 2002 Chevrolet Impala
Check engine light on? If so post scan test results.
Have drive axles checked for inner tripod wear.
Check engine light is not on. Last time it was on about 6 months ago it was for a minor issue. Service engine soon light has been on for a couple of years, well over 50,000 miles. Two Chevy dealers and 2 independent garages have found no issues and have been unable to turn it off.
1- possible engine misfire.
2- possible drive axle wear.
See your mechanic!
Thank you, will do. Should I have both axles checked? Also, about how much should they charge to check them Would this also cause extreme shaking sometimes when I brake?
No only when accelerating. Brake rotor run out most likely excessive!
Thanks for your help. I'll get the axles checked out, I posted on this site because the I thought this new problem with the clunking noise and shaking when using the accelerator could be a major issue. I knew the rear brakes were due to be replaced soon, so I'll get that done too. Thanks again. Now I can go in with an idea of what needs be checked out first.