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

**URL:** <https://community.wolfram.com/t/integration-error-invalid-integration-variable-or-limit-s/17720>\
**Category:** Questions\
**Tags:** calculus, symbolic-computations\
**Created:** [March 3, 2021, 2:04am UTC](https://community.wolfram.com/t/integration-error-invalid-integration-variable-or-limit-s/17720 "2021-03-03T02:04:01Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![alongcamp](https://avatars.discourse-cdn.com/v4/letter/a/7993a0/32.png) [@alongcamp](https://community.wolfram.com/u/alongcamp)\
**Post date:** [March 3, 2021, 2:04am UTC](https://community.wolfram.com/t/integration-error-invalid-integration-variable-or-limit-s/17720/1 "2021-03-03T02:04:01Z")

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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](https://community.wolfram.com/uploads/short-url/8SUZlzvn8Bmg9n5YSQS3rwlxh3k.nb) (6.55 KB)

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<div class="post-metadata">

**Author:** ![mariuszi28cg](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/mariuszi28cg/32/308_2.png) [@mariuszi28cg](https://community.wolfram.com/u/mariuszi28cg)\
**Post date:** [March 3, 2021, 1:56pm UTC](https://community.wolfram.com/t/integration-error-invalid-integration-variable-or-limit-s/17720/2 "2021-03-03T13:56:42Z")

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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**.

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<div class="post-metadata">

**Author:** ![kiwee](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/kiwee/32/9383_2.png) [@kiwee](https://community.wolfram.com/u/kiwee)\
**Post date:** [March 3, 2021, 11:08pm UTC](https://community.wolfram.com/t/integration-error-invalid-integration-variable-or-limit-s/17720/3 "2021-03-03T23:08:34Z")

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The integrand looks off. Just a feeling.

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<div class="post-metadata">

**Author:** ![claudemante1](https://avatars.discourse-cdn.com/v4/letter/c/c6cbf5/32.png) [@claudemante1](https://community.wolfram.com/u/claudemante1)\
**Post date:** [March 4, 2021, 10:23am UTC](https://community.wolfram.com/t/integration-error-invalid-integration-variable-or-limit-s/17720/4 "2021-03-04T10:23:39Z")

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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

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<div class="post-metadata">

**Author:** ![alongcamp](https://avatars.discourse-cdn.com/v4/letter/a/7993a0/32.png) [@alongcamp](https://community.wolfram.com/u/alongcamp)\
**Post date:** [March 4, 2021, 2:53pm UTC](https://community.wolfram.com/t/integration-error-invalid-integration-variable-or-limit-s/17720/5 "2021-03-04T14:53:31Z")

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Thank you so much!!