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(2*(1 + x)^(3/2)*(-2 + 3*x))/15

Integrate[x*Sqrt[1 + x], x] ==
(2*(1 + x)^(3/2)*(-2 + 3*x))/15 

Integrate[x Sqrt[1 + x], x] == 

         3/2
2 (1 + x)    (-2 + 3 x)
-----------------------
          15
Time to compute: < 0.01 second
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