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(2*(a + b*x)^(3/2)*(8*a^2 - 12*a*b*x + 15*b^2*x^2))/(105*b^3)

Integrate[x^2*Sqrt[a + b*x], x] ==
(2*(a + b*x)^(3/2)*(8*a^2 - 12*a*b*x + 15*b^2*x^2))/ (105*b^3) 

           2
Integrate[x  Sqrt[a + b x], x] == 

           3/2     2                  2  2
2 (a + b x)    (8 a  - 12 a b x + 15 b  x )
-------------------------------------------
                       3
                  105 b
Time to compute: 0.03 second
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