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

                  1/3
          (-a + x)
Integrate[-----------, x] == 
               x

          1/3            1/3
3 (-a + x)    + Sqrt[3] a    
 
                        1/3
              2 (-a + x)
          1 - -------------
                   1/3
                  a
   ArcTan[-----------------] - 
               Sqrt[3]
 
   1/3      1/3           1/3
  a    Log[a    + (-a + x)   ] + 
 
   1/3      2/3    1/3         1/3           2/3
  a    Log[a    - a    (-a + x)    + (-a + x)   ]
  -----------------------------------------------
                         2