Integration error: "Invalid integration variable or limit(s)"

Questions
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1

Hello all,

I was wondering if someone could help me fix the attached code? I am trying to use the “Assumptions” argument such that my lower bound > upper bound > 0.

Thank you,

Alex

Not working.nb (6.55 KB)

2

Do you have any reason to think there is a closed form? Most integrals don’t have one. Maybe the best you can do is numerical methods.Try: NIntegrate.

3

The integrand looks off. Just a feeling.

4

Hi!

I tried to simply your problem, using the linearity of the integral.
First,

IntegListe = 
 Apply[List, 
  ExpandAll[
   K*(a*K*Exp[-(a + ((g*(1 - c*g))*(L/(1 + (L - 1)*Exp[-(t - T)])))/
              K)*t] + (g*(1 - 
            c*g))*(L/(1 + (L - 1)*Exp[-(t - T)])))/(a*
        K + (g*(1 - c*g))*(L/(1 + (L - 1)*Exp[-(t - T)])))]]

gives 3 functions, which can be integrated separately, and added afterwards. As for the third one,
we have:

In[21]:= Integrate[IntegListe[[3]], {t, T, Q}, 
 Assumptions -> Q > T > 0]

Out[21]= (c g^2 K L (T + Log[(g (-1 + c g) - a K) L] - 
   Log[-a K (E^Q + E^T (-1 + L)) + E^Q g (-1 + c g) L]))/(
a K + g (1 - c g) L)

so, it has a closed form. The second member has a closed form, too, contrary to the first one:

In[24]:= Integrate[FullSimplify[IntegListe[[1]]], {t, T, Q}, 
 Assumptions -> Q > T > 0]

Out[24]= Integrate[(
 a E^(-a t + (E^t g (-1 + c g) L t)/(K (E^t + E^T (-1 + L))))
   K^2 (E^t + E^T (-1 + L)))/(
 a E^T K (-1 + L) + E^t (a K + g (1 - c g) L)), {t, T, Q}, 
 Assumptions -> Q > T > 0]

Consequently, I think you should focus on this first function (simplify it, approximate by a convergent series, etc).

Hope this helps!

Claude

5

Thank you so much!!