Hi,
Tne integral can be expanded as:
Integrate[ x^h*E^-((?*x) + (?*x^n))*(DiracDelta[x]*x^t* E^(-?*x^m)), {x, 0, ?}] +
Integrate[ x^h*E^-((?*x) + (?*x^n)), {x, 0, ?}]
The first integral can be easily evaluated using the properties of the DiracDelta function. However, Mathematica does not evaluate the second integral in closed form for general parameters n and h. Closed form results may be obtained if the parameters are given specific values.
Youngjoo Chung