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-(-3*Log[x] + Log[c^3 + x^3])/(3*c^3)

Integrate[1/(x*(c^3 + x^3)), x] ==
-(-3*Log[x] + Log[c^3 + x^3])/(3*c^3) 

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

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