# Integrate the following exponential function?

**URL:** <https://community.wolfram.com/t/integrate-the-following-exponential-function/15835>\
**Category:** Questions\
**Tags:** calculus\
**Created:** [April 23, 2020, 4:52am UTC](https://community.wolfram.com/t/integrate-the-following-exponential-function/15835 "2020-04-23T04:52:17Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![hien1996dhsphue](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/hien1996dhsphue/32/27092_2.png) [@hien1996dhsphue](https://community.wolfram.com/u/hien1996dhsphue)\
**Post date:** [April 23, 2020, 4:52am UTC](https://community.wolfram.com/t/integrate-the-following-exponential-function/15835/1 "2020-04-23T04:52:17Z")

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Consider the following code:

```
Integrate[
         Exp[-u]*Sqrt[
           u*(u - a)]*(-2*Power[b, 3]/(4*u*b + Power[a - b, 2])), {u, 0, 
          Infinity}]

```

I am a beginner. Since I want to solve the above integration, but I don not know the reason why Mathematica (ver.12) did not display the symbolic result which I want to do.  
So I hope that have any idea to solve this integration.  
Thank you very much.

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**Author:** ![nikolayshilov1997](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/nikolayshilov1997/32/7843_2.png) [@nikolayshilov1997](https://community.wolfram.com/u/nikolayshilov1997)\
**Post date:** [April 23, 2020, 9:12am UTC](https://community.wolfram.com/t/integrate-the-following-exponential-function/15835/2 "2020-04-23T09:12:31Z")

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I am not an expert in calculus, but I doubt if this integral can be expressed in any terms except of the input integral for arbitrary _a_ and _b_.

For instance, if one substitutes _a = - 1_ and _b = 1_ he / she will get **HypergeometricU** in the result. Using _a = 0_ instead leads to **ExpIntegralEi**. And setting _a_ to _1_ results in unevaluated integral.

In any case, if _a_ and _b_ are not arbitrary I suggest using **Assumptions** option inside the **Integrate** function.

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<div class="post-metadata">

**Author:** ![hien1996dhsphue](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/hien1996dhsphue/32/27092_2.png) [@hien1996dhsphue](https://community.wolfram.com/u/hien1996dhsphue)\
**Post date:** [April 23, 2020, 9:31am UTC](https://community.wolfram.com/t/integrate-the-following-exponential-function/15835/3 "2020-04-23T09:31:41Z")

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Yes, thank you very much for your helpful information. In my case, a and b are not arbitrary.