Is the textbook's answer correct?

  • Thread starter GregA
  • Start date
In summary, the conversation is about integrating the expression (x+1)/x(2x+1) with respect to x by using partial fractions. The person has correctly found the partial fraction decomposition and integrated the expression, but their answer differs from the book's answer. The person questions if there is a mistake in their working or if the book's answer is incorrect. The summary concludes that the book's answer is wrong.
  • #1
GregA
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0
A pretty simple question that is doing my head in is the folllowing:
Integrate (x+1)/x(2x+1) w.r.t.x
by choosing to use partial fractions of the form A/x + B/2x+1 my working is as follows:
using the cover up method and x = 0 to find A I get A =1 ...(0+1)/(2(0)+1)
using x = -1/2 to find B I get B = -1...((-1/2+1)/-1/2)
this leaves me with 1/x - 1/(2x+1) to be integrated.
my answer being lnA + lnx +1/2ln(2x+1) or lnA(x/((2x+1)^(1/2)) (because 1 is half the derivative of 2x)...the books answer is simply ln(x/2x+1)...they omit the constant by specifying that all answers should include it...My question is: is there something wrong with my working or is the book's answer wrong and I should move on?
 
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  • #2
You have the partial fraction decomposition right, and you've integrated correctly (except for a typo). It looks like the book answer is wrong.
 
  • #3
grrrr nasty textbook! Cheers PhysicsMonkey :smile:
 

1. Is the textbook's answer always correct?

No, the textbook's answer may not always be correct. Textbooks are written by humans and can contain errors or outdated information. It is always important to double check the information and verify it from reliable sources.

2. Can I trust the textbook's answer?

Yes, textbooks are generally considered trustworthy sources of information. However, it is always important to critically evaluate the information and cross-check it with other sources to ensure accuracy.

3. What should I do if I think the textbook's answer is wrong?

If you believe the textbook's answer is incorrect, you should bring it to the attention of your teacher or instructor. They can review the information and provide clarification or corrections if needed.

4. How do I know if the textbook's answer is up-to-date?

Textbooks are often updated with new editions to keep the information current. You can check the publication date of the textbook to determine if the answer is up-to-date. Additionally, you can research the topic further to see if there have been any recent developments or changes.

5. Can I use the textbook's answer as a reliable source in my research or experiments?

It is generally acceptable to use the textbook's answer as a source in your research or experiments. However, it is important to cite the textbook and also cross-check the information with other reputable sources to ensure accuracy. Additionally, for scientific experiments, it is always best to follow the instructions and guidelines provided by your teacher or instructor.

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