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Integrate[E^x*x^20, x] ==
E^x*(2432902008176640000 - 2432902008176640000*x + 1216451004088320000*x^2 - 405483668029440000*x^3 + 101370917007360000*x^4 - 20274183401472000*x^5 + 3379030566912000*x^6 - 482718652416000*x^7 + 60339831552000*x^8 - 6704425728000*x^9 + 670442572800*x^10 - 60949324800*x^11 + 5079110400*x^12 - 390700800*x^13 + 27907200*x^14 - 1860480*x^15 + 116280*x^16 - 6840*x^17 + 380*x^18 - 20*x^19 + x^20)

           x  20
Integrate[E  x  , x] == 

 x
E  (2432902008176640000 - 2432902008176640000 x + 
 
                         2                       3
    1216451004088320000 x  - 405483668029440000 x  + 
 
                        4                      5
    101370917007360000 x  - 20274183401472000 x  + 
 
                      6                    7
    3379030566912000 x  - 482718652416000 x  + 
 
                    8                  9
    60339831552000 x  - 6704425728000 x  + 
 
                  10                11
    670442572800 x   - 60949324800 x   + 
 
                12              13             14
    5079110400 x   - 390700800 x   + 27907200 x   - 
 
             15           16         17        18
    1860480 x   + 116280 x   - 6840 x   + 380 x   - 
 
        19    20
    20 x   + x  )