Integrating 1/x*e^x dx from 0 to s, how to do it

In summary, the conversation is about integrating a function with a specific upper bound and finding a way to exclude that bound from the integral. There is also a discussion about changing parameters of integration.
  • #1
smoodliar
4
0
Hi

I have an integral as follows,

int((1/x)exp(-x),x,0,s)

I want to integrate from [0,s).

My question is how to integrate without including s as the upper bound.

Any help will be appreciated
 
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  • #2


Integrate from [0,s-a] in the limit as a -> 0?
 
  • #3


Hey

Thanks for the reply.

If the integral is the lower gamma incomplete function, which is

int(exp(-t)*t^(a-1),t,0,x)

how would I be able to evaluate the integral between [0,x-a) as a->0 ?
 
  • #4


Feldoh said:
Integrate from [0,s-a] in the limit as a -> 0?

well u are right

but i don't know, his question doest sound too sensible to me

then by anser u gave it obviously means changing parameters of integration
 
  • #5


Hi sachinism

I hope I cleared up my question with my last post.

Any help will be great
 

1. What is the purpose of integrating 1/x*e^x dx from 0 to s?

The purpose of this integration is to find the area under the curve of the function 1/x*e^x from 0 to s. This is a common problem in calculus and has many real-world applications, such as calculating the growth rate of a population or the amount of medication needed for a patient over time.

2. What is the process of integrating 1/x*e^x dx from 0 to s?

The process of integrating this function involves using the integration by parts technique. This involves breaking the function into two parts, one of which is the derivative of the other. By applying this technique, the integral can be simplified and solved using basic integration rules.

3. Can the integration of 1/x*e^x dx from 0 to s be solved without using integration by parts?

Yes, there are alternative methods for solving this integral, such as using substitution or trigonometric identities. However, integration by parts is the most common and efficient method for solving this particular integral.

4. Are there any special cases or exceptions when integrating 1/x*e^x dx from 0 to s?

Yes, if the upper limit of integration (s) is equal to 0, the integral will be undefined as it results in division by 0. Additionally, if s is a negative value, the integral will also be undefined as the function 1/x is not defined for negative values.

5. How can I check if my integration of 1/x*e^x dx from 0 to s is correct?

You can check your integration by taking the derivative of the result and comparing it to the original function. If the two are equivalent, then your integration is correct. Additionally, you can use online integration calculators or ask a math tutor for verification.

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