1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Integration using natural logs, halp! (beginning of my calc 2 class)

  1. Jan 20, 2013 #1
    1. The problem statement, all variables and given/known data
    Ok, so I have the problem, and I have the answer, but I don't know how they arrived at the answer. I'll show you the problem, and what I tried and maybe somebody can point out where I am going wrong, or some hints to put me on the right path.

    (2x-1)/(x+1) being integrated on ∫ 0 to 6

    this lesson is supposed to be demonstrating how to integrate using natural log.

    The answer I was given was

    12-3 ln 7

    3. The attempt at a solution

    I tried a variety of things, none of which led me to the given solution. I tried breaking it up into (2x)/(x+1)-(1)/(x+1) and then integrating each piece (which I'm not sure is a "legal" move) getting x^2 ln (x+1)-x ln (x+1), or trying it as x^2-x ln (x+1) neither of which gets me to the final answer.

    Now there was a hint to use "U substitution" but I had in the past been told that I can only do "u substitution" if the derivative is found elsewhere in the function or the derivative is off by a constant factor. the derivative of neither expression is the other off by a constant factor (they would both be off by a variable x), so I'm not sure how to do a "u substitution" in that case. Halp?
  2. jcsd
  3. Jan 20, 2013 #2


    User Avatar
    Science Advisor
    Homework Helper

    Put u=(x+1). Then du=dx and x=(u-1). Substitute that into 2x-1 to get the numerator in terms of u.
  4. Jan 20, 2013 #3


    User Avatar
    Homework Helper

    $$\int_0^6 \! \frac{2x-1}{x+1}\, \mathrm{dx}=\int_0^6 \! \frac{2(x+1)-3}{x+1}\, \mathrm{dx}=\int_0^6 \! \left(2-3\frac{1}{x+1} \right)\, \mathrm{dx}$$
  5. Jan 24, 2013 #4
    Oh, I forgot to thank you guys. That totally cleared up that problem and helped alot with methods for a couple of other ones. Thanks gentlemen!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook