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
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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.