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(3*((E + (c + d)*x)^(1/3)*(-2*a - 2*b + (E + (c + d)*x)^(1/3)) + 2*(a + b)^2*Log[a + b + (E + (c + d)*x)^(1/3)]))/(2*(c + d))


Integrate[1/(a + b + (E + c*x + d*x)^(1/3)), x] ==
(3*((E + (c + d)*x)^(1/3)*(-2*a - 2*b + (E + (c + d)*x)^(1/3)) + 2*(a + b)^2* Log[a + b + (E + (c + d)*x)^(1/3)]))/(2*(c + d))



                      1
Integrate[--------------------------, x] == 
                                 1/3
          a + b + (E + c x + d x)

                   1/3
(3 ((E + (c + d) x)    
 
                                    1/3
       (-2 a - 2 b + (E + (c + d) x)   ) + 
 
               2                            1/3
      2 (a + b)  Log[a + b + (E + (c + d) x)   ])) / 
 
  (2 (c + d))

Time to compute: 0.13 second

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