What is the correct way to find the indefinite integral of e^(6x)/(e^(6x)+6)?

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Discussion Overview

The discussion revolves around finding the indefinite integral of the function e^(6x)/(e^(6x)+6) with respect to x. Participants are exploring the correct approach to this integral, addressing potential mistakes and clarifying notation used in online homework submissions.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents an initial solution for the integral, suggesting it equals 1/6*(ln(e^6x+6)) + C, but expresses uncertainty about its correctness.
  • Another participant questions the reasoning behind the initial participant's belief that their solution is incorrect.
  • A participant mentions that their online homework platform indicates the solution is wrong and requests assistance in identifying the mistake.
  • One suggestion is made that the online answer may require the absolute value of (e^6x + 6) in the logarithm, although it is noted that this is not necessary since (e^6x + 6) is always positive.
  • There is a discussion about the conventions used in the online platform, including the notation for the constant "C" and the potential confusion between "log" and "ln".
  • Another participant raises a concern about the multiplication notation required by the web interface, suggesting that improper notation could lead to the answer being marked incorrect.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct form of the integral or the specific requirements of the online homework platform. Multiple competing views regarding notation and the correctness of the initial solution remain unresolved.

Contextual Notes

There are limitations regarding the assumptions about notation and the specific requirements of the online homework system, which may affect the interpretation of the solution.

Zvaigzdute
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Hi I have to find the indefinete integral of

e^(6x)/(e^(6x)+6)*dx

And I get

1/6*(ln(e^6x+6)) +C

What am I doing wrong?

Thank you
 
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Why do you think it has gone awry? :smile:
 
All of my calculus homework is submitted online to Web assign, and the website says that this is wrong. I cannot see where I may have made a mistake, and I was wondering if somebody could point it out, and show me how to get to the right answer
 
Perhaps the online answer is looking for an absolute value of the quantity (e^6x + 6) in the argument of the ln in your answer?

You are justified in removing the absolute value, since
(e^6x + 6) > 0 for all real x.
 
Zvaigzdute said:
All of my calculus homework is submitted online to Web assign, and the website says that this is wrong. I cannot see where I may have made a mistake, and I was wondering if somebody could point it out, and show me how to get to the right answer
1. Is the conventional Web Assign code for the undetermined constant "C"?

2. Sometimes, "log" is used as denoting "ln", since Briggsian logarithms are beyond moribund.
 
(1) Do you have to write * for multiply on that web interface? If so, your answer does not qualify.

(2) If you write e^6x it probably means (e^6)*x, and that is certainly wrong.
 

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