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Integrate[Sqrt[1 + E^(c + 5*x) + E^(-d + 10*x)], x] ==
Sqrt[1 + E^(c + 5*x) + E^(-d + 10*x)]/5 + x - Log[5*(2 + E^(c + 5*x) + 2*Sqrt[1 + E^(c + 5*x) + E^(-d + 10*x)])]/5 + (E^(c + d/2)*Log[E^c + 2*E^(-d + 5*x) + (2*Sqrt[1 + E^(c + 5*x) + E^(-d + 10*x)])/ E^(d/2)])/10



                    c + 5 x    -d + 10 x
Integrate[Sqrt[1 + E        + E         ], x] == 

          c + 5 x    -d + 10 x
Sqrt[1 + E        + E         ]
------------------------------- + x - 
               5
 
              c + 5 x
  Log[5 (2 + E        + 
 
                   c + 5 x    -d + 10 x
       2 Sqrt[1 + E        + E         ])] / 5 + 
 
    c + d/2      c      -d + 5 x
  (E        Log[E  + 2 E         + 
 
                   c + 5 x    -d + 10 x
       2 Sqrt[1 + E        + E         ]
       ---------------------------------]) / 10
                      d/2
                     E

Time to compute: 0.32 second

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