How would I go around integrating $$\int_0^\infty \left( \exp{\left(-\int_{k_0}^{k_0+t} (k_1 + k_2s)(k_3+k_4s)^{s} ds \right) } \right) dt \text{,}$$ where $k_i$ are constants?
Is it solvable analytically? If not, is the following integral $$\int_0^n \left( \exp{\left(-\int_{k_0}^{k_0+t} (k_1 + k_2s)(k_3+k_4s)^{s} ds \right) } \right) dt \text{,}$$ where $n \in \mathbb{R}^+$?
I have little idea on how to approach it since I only have a year of calculus behind me. However, I need to evaluate these integrals in any case so what is the best method to do it numerically, if they are not solvable?
EDIT: Instead of $k_0+s$ there should be just $s$ in the exponent of $k_3 + k_4s$, I corrected this in the original question.