How to do the indefinite integral

Click For Summary

Homework Help Overview

The discussion revolves around finding the indefinite integral of an improper integral involving the expression integral[e^(1/x)/x^3]. Participants are exploring various methods to approach this integral.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts integration by parts, substitution, and reference to a table of integrals without success. Some participants suggest splitting the integral and applying integration by parts, while others propose a U substitution approach, identifying u as 1/x and deriving the corresponding du.

Discussion Status

Some participants have provided guidance on potential methods, including integration by parts and U substitution. There appears to be a productive exchange of ideas, with at least one participant indicating that the substitution method was successful.

Contextual Notes

The original poster expresses difficulty with the integral, indicating a lack of clarity on how to proceed, which may reflect constraints in their understanding or the complexity of the integral itself.

cloudage
Messages
14
Reaction score
0

Homework Statement


I hope someone can help me with this integral. It is really an improper integral, but I cannot figure out how to do the indefinite integral on it:

integral[e1/x/x3].

Any help would be appreciated, thanks.



Homework Equations


?


The Attempt at a Solution



I tried integration by parts, substitution and using the table of integrals. I couldn't get any of them to work.
 
Physics news on Phys.org


I would be included to split it up as (1/x) *[ (1/x^2)*e^(1/x)] and try integration by parts on that. IOW, u = 1/x, and dv = (1/x^2)*e^(1/x)dx.

I don't know that this would work, but that's what I would start with.
 


This is definitely a U substitution problem, when things are kinda odd inside an exponential, its the best method to try.

pick u=1/x,
that means du= (-1/x^2) dx.

so
\int \frac{e^{1/x}}{x^{3}} dx = \int \frac{-1}{x} e^{1/x}(\frac{-1}{x^{2}}dx)
 


Thank you so much! The substitution did the trick!
 


perfect. Now if only I could get help with my cray cray math.
 

Similar threads

  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
Replies
11
Views
2K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 12 ·
Replies
12
Views
2K
Replies
12
Views
3K
  • · Replies 11 ·
Replies
11
Views
1K
Replies
10
Views
2K