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Limit[     (Integrate[Sqrt[Exp[3 t + 2] + 3] , {t, 0, x}]^2)   / 
  Integrate[Sqrt[Exp[6 t - 2] + 5] , {t, 0, x}] , x -> 0]Infinity]

This can be solved but mathematica cant give a result. Why ?

Limit[     (Integrate[Sqrt[Exp[3 t + 2] + 3] , {t, 0, x}]^2)   / 
  Integrate[Sqrt[Exp[6 t - 2] + 5] , {t, 0, x}] , x -> 0]

This can be solved but mathematica cant give a result. Why ?

Limit[     (Integrate[Sqrt[Exp[3 t + 2] + 3] , {t, 0, x}]^2)   / 
  Integrate[Sqrt[Exp[6 t - 2] + 5] , {t, 0, x}] , x -> Infinity]

This can be solved but mathematica cant give a result. Why ?

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Calculate this integral returns undefined

Limit[     (Integrate[Sqrt[Exp[3 t + 2] + 3] , {t, 0, x}]^2)   / 
  Integrate[Sqrt[Exp[6 t - 2] + 5] , {t, 0, x}] , x -> 0]

This can be solved but mathematica cant give a result. Why ?