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(b*x*(-2*a + b*x) + 2*a^2*Log[a + b*x])/(2*b^3)

Integrate[x^2/(a + b*x), x] ==
(b*x*(-2*a + b*x) + 2*a^2*Log[a + b*x])/(2*b^3) 

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

                      2
b x (-2 a + b x) + 2 a  Log[a + b x]
------------------------------------
                   3
                2 b
Time to compute: < 0.01 second
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