Evaluating an integral symbolically

Question

I am trying to integrate following integral symbolically via integrate command:

$$(0.09)\Bigg[1 + \Bigg\{ \int_{3t-4k-7}^{2k+7/3} (0.09) \text{exp}\Bigg(\int_{3s-4k-7}^{2k+7/3} (0.09) \text{exp}\Bigg(\int_{3u-4k-7}^{2k+7/3}(0.09)d\xi \Bigg)du\Bigg)ds\Bigg\} \Bigg]$$

but it gives a result like this:

$$0.09(1+0.06(-1.56+1.23\text{ExpIntegralEi}[1482e^{4.82k-2.43t}]$$

and I can't evaluate this expression further even if I substitute integers with $k$.

How can I proceed further of this expression?

Edit: Mathematica code

integral1 = \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(3  u - 4  k - 7\), \(2  k + 
    7/3\)]\(\((0.09)\) \[DifferentialD]\[Xi]\)\)

integral2 = \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(3  s - 4  k - 7\), \(2  k + 
    7/3\)]\(\((0.09)\) Exp[integral1] \[DifferentialD]u\)\)

integral3 = \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(3  t - 4  k - 7\), \(2  k + 
    7/3\)]\(\((0.09)\) Exp[integral2] \[DifferentialD]s\)\)
```

Answer 1

Try:

$Version
(* "12.0.0 for Microsoft Windows (64-bit) (April 6, 2019)" *)

Integrate[(9/100)*Exp[Integrate[(9/100)*Exp[Integrate[9/100, {ξ, 3*u - 4*k - 7, 2*k + 7/3}]],
{u, 3*s - 4*k - 7, 2*k + 7/3}]], {s, 3*t - 4*k - 7, 2*k + 7/3}]

(*ConditionalExpression[-(1/9) E^(-(E^(21/100)/3)) (ExpIntegralEi[E^(21/25)/3] - 
ExpIntegralEi[1/3 E^(3/100 (280 + 162 k - 81 t))]), E^(162 k - 81 t) >= 0]*)


%[[1]] /. k -> 1 /. t -> 1(*I assume for k and t *)

(*  -(1/9) E^(-(E^(21/100)/3)) (ExpIntegralEi[E^(21/25)/3] - ExpIntegralEi[E^(1083/100)/3]) *)

$$-\frac{1}{9} e^{-\frac{e^{21/100}}{3}} \left(\text{Ei}\left(\frac{e^{21/25}}{3}\right)-\text{Ei}\left(\frac{e^{1083/100}}{3}\right)\right)$$