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Hi I have a function in a form of


$$\frac{a}{x}exp(\frac{b}{\sqrt{3}-x})$$


The code is

Integrate[a/x*E^(b/(3^0.5 - x)), {x, 1, 3^0.5}]

But it can't work currently, even given the value of a and b. Can it be integrated by Mathematica? How can I get the approximation (or if you have the method to get exact integration) and plot the diagram?

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closed as off-topic by Öskå, rasher, Yves Klett, Kuba, Oleksandr R. Jun 17 at 11:38

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question arises due to a simple mistake such as a trivial syntax error, incorrect capitalization, spelling mistake, or other typographical error and is unlikely to help any future visitors, or else it is easily found in the documentation." – Öskå, rasher, Yves Klett, Kuba, Oleksandr R.
If this question can be reworded to fit the rules in the help center, please edit the question.

    
Is your question related with the software Mathematica? If so, please provide the code for this function in a Mathematica form. –  Öskå Jun 17 at 9:29
    
@Öskå I was wondering whether that can be integrated by mathematica. –  Jack Zhang Jun 17 at 9:30
    
I am not sure that it is not an off-topic. Otherwise, the statement of the question should be done more precise ( integral in which limits?) and written down a Mma expression. –  Alexei Boulbitch Jun 17 at 9:31
    
@AlexeiBoulbitch Thanks, just updated. Is this kind of problem not integratable by mathematica? At least, I think it can solve it numerically for given value and limit, but how to do it? –  Jack Zhang Jun 17 at 9:42
1  
It's Exp[] not E^: see here. –  Öskå Jun 17 at 9:49

1 Answer 1

up vote 1 down vote accepted

With 9.01:

int = Integrate[a/x*E^(b/(3^0.5 - x)), {x, 1, 3^0.5}]

ConditionalExpression[ a (1. ExpIntegralEi[1.36603 b] + E^(0.57735 b) (-1. ExpIntegralEi[0.788675 b] + 1. ExpIntegralEi[7.88675*10^8 b]) - 1. ExpIntegralEi[7.88675*10^8 b]), Re[b] <= 0]

Plot3D[int, {a, -10, 10}, {b, -3, 0}, ColorFunction -> "DarkRainbow", 
 Mesh -> False]

enter image description here

Update

For positive b the Integral does not converge (see above Re[b] <= 0):

a = 1; b = 1;

Integrate[a/x*E^(b/(3^0.5 - x)), {x, 1, 3^0.5}]

enter image description here

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Thanks a lot, it looks amazing! Is it possible to plot the integration diagram to represent function changing with x, with given a and b (for example a=b=1)? –  Jack Zhang Jun 17 at 10:16
    
@JackZhang - see updated answer –  eldo Jun 17 at 10:29
    
Yep, for x close to the $$\sqrt{3}$$, the function is approach to infinite. –  Jack Zhang Jun 17 at 12:06
    
@Jack Zhang Why do not you try NIntegrate at a and b of your choice. Then you will easily see what is possible, or at least, what is impossible? –  Alexei Boulbitch Jun 17 at 13:03
    
@AlexeiBoulbitch Good ideal, I'll have a try. –  Jack Zhang Jun 18 at 1:34

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