Integrate special function

Question

I have the following integral $$ \int_a^b e^{\alpha_1 x + \alpha_2 x^2 + \alpha_3 e^{-\beta x}} dx, \\ \text{where} \, \alpha_1, \alpha_2, \alpha_3 \,\text{and} \, \beta \, \text{are constants} $$ I´ve tried to solve with Mathematica, but it was not possible. So, I´ve tried manually making a change of variable $$v=e^{-\beta x} $$ but I obtain other expression complicated $$\int_c^d v^{\theta_1 \ln v}e^{\theta_2 v^{\theta_3}}dv \\ \text{where} \, \theta_1, \theta_2 \,\text{and} \, \theta_3 \, \text{are constants}$$ wich is also impossible for Mathematica. Any suggestion? Thanks