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
210
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:
 

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