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Integrate[x^9*Sqrt[2*a*x - x^2], x] ==
(Sqrt[-(x*(-2*a + x))]*(Sqrt[x]*Sqrt[-2*a + x]* (-14549535*a^10 - 4849845*a^9*x - 1939938*a^8*x^2 - 831402*a^7*x^3 - 369512*a^6*x^4 - 167960*a^5*x^5 - 77520*a^4*x^6 - 36176*a^3*x^7 - 17024*a^2*x^8 - 8064*a*x^9 + 80640*x^10) - 29099070*a^11* Log[2*(Sqrt[x] + Sqrt[-2*a + x])]))/ (887040*Sqrt[x]*Sqrt[-2*a + x])



           9               2
Integrate[x  Sqrt[2 a x - x ], x] == 

(Sqrt[-(x (-2 a + x))] 
 
    (Sqrt[x] Sqrt[-2 a + x] 
 
                   10            9
       (-14549535 a   - 4849845 a  x - 
 
                  8  2           7  3
         1939938 a  x  - 831402 a  x  - 
 
                 6  4           5  5          4  6
         369512 a  x  - 167960 a  x  - 77520 a  x  - 
 
                3  7          2  8           9
         36176 a  x  - 17024 a  x  - 8064 a x  + 
 
                10
         80640 x  ) - 
 
                11
      29099070 a   Log[2 (Sqrt[x] + Sqrt[-2 a + x])]))
 
    / (887040 Sqrt[x] Sqrt[-2 a + x])

Time to compute: 0.37 second

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