How do I integrate (1+(1/x))^x?

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Homework Help Overview

The problem involves integrating the expression ∫(1+(1/x))^x dx, which relates to concepts in calculus and potentially compound interest approximations.

Discussion Character

  • Exploratory, Assumption checking, Mixed

Approaches and Questions Raised

  • Participants discuss the possibility of a closed form for the integral, with some expressing skepticism about its existence. Others mention the use of a TI-84 calculator for evaluating definite integrals and inquire about the specific limits of integration.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem. Some have provided guidance on using calculators for definite integrals, while others are questioning the nature of the integral itself.

Contextual Notes

There is mention of the original poster's limited experience with integration, and the discussion includes considerations of both symbolic and numerical answers.

Phys_Boi
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Homework Statement


∫(1+(1/x))^x dx

Homework Equations


How do I integrate this compound interest e approximation

The Attempt at a Solution


Inside: x + ln(|x|) + C
Outside: (a^x)/(ln(a))
 
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I would be extremely susprised if it has a closed form for the integral.
 
mfb said:
I would be extremely susprised if it has a closed form for the integral.
Thanks. I'm new and don't know a lot.. However the ti-84 will give me a value for a definite integral. I don't know how.
 
Phys_Boi said:
Thanks. I'm new and don't know a lot.. However the ti-84 will give me a value for a definite integral. I don't know how.

Exactly what definite integral are you entering? That is, what are the integration limits? Is the answer "symbolic" or "numerical"?
 
A specific definite integral can be way easier than an analytic expression for the indefinite integral.
 
Oh okay. Thanks.
 

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