Integral with e^x: Solving for ln(e^2x + 1)

  • Thread starter Thread starter Michael Gulley
  • Start date Start date
  • Tags Tags
    E^x Integral
Click For Summary

Homework Help Overview

The problem involves evaluating the integral ∫(2e^x)/(e^x+e^-x)dx and aims to arrive at the result ln(e^2x + 1). The original poster expresses difficulty in achieving the correct result and mentions consistently obtaining (e^2x)ln(e^2x + 1).

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants suggest simplifying the integral and considering u-substitution. There is also a hint regarding the derivative of e^2x, which may relate to the original poster's misunderstanding. One participant proposes multiplying the numerator and denominator by e^x to facilitate the integration process.

Discussion Status

The discussion is ongoing, with various participants providing hints and suggestions for approaching the integral. There is no explicit consensus on the correct method yet, but several productive directions have been proposed.

Contextual Notes

The original poster has not provided their work, which limits the ability of others to identify specific errors in their reasoning. This absence of detail may affect the clarity of the discussion.

Michael Gulley
Messages
1
Reaction score
0
The problem I have is

∫(2e^x)/(e^x+e^-x)dx

I cannot seem to get to the correct result, ln(e^2x + 1). I always have (e^2x)ln(e^2x + 1). What do I need to do, to get rid of the e^2x.
Any help would be greatly appreciated.
 
Physics news on Phys.org
Do the problem correctly. How's that for a nice vague reply? Unfortunately, that's about all anyone can say without seeing your work. How are we supposed to see where you're going wrong if you don't show your work?
 
Step 1. Try to simplify the problem (i.e., take any constants out of the integral).

Step 2. You may want to try u-substitution.
 
Hint: What's the derivative of e^2x?

I think this is probably where the mistake was made.
 
Its simple. Multiply your numerator and denominator by e^x. This will get you (2e^2x)/(e^2x + 1)dx. Now suppose your whole denominator as another variable,say, t. Calculate dt which will be equal to 2e^2xdx.
So now your integral is in the form of (1/t)dt. Integration of this will give you ln(t). Substitute back the value of 't' and there you have it.
 

Similar threads

  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 4 ·
Replies
4
Views
1K
Replies
2
Views
1K
Replies
7
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 14 ·
Replies
14
Views
2K
Replies
4
Views
2K
  • · Replies 26 ·
Replies
26
Views
2K