Results 1 to 5 of 5

Math Help - log rule for integration confusion

  1. #1
    Member
    Joined
    Oct 2009
    Posts
    195
    Thanks
    1

    log rule for integration confusion

    If I have a function:

    f(x) = 1 / (x+1), and I want to find it's indefinite integral, I can apply the log rule and get:

    F(x) = ln |x+1| + C

    If, however, I multiply both the numerator and the denominator by 2, before integrating, I get:

    f(x) = 1 / (x+1) = 2 / 2x + 2

    F(x) = ln |2x+2| + C

    Clearly, f(x) are equal in both cases, but I can't see how ln |2x+2| equals ln |x+1|

    Any explanation? Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1

    Re: log rule for integration confusion

    Quote Originally Posted by gralla55 View Post
    If I have a function:

    f(x) = 1 / (x+1), and I want to find it's indefinite integral, I can apply the log rule and get:

    F(x) = ln |x+1| + C

    If, however, I multiply both the numerator and the denominator by 2, before integrating, I get:

    f(x) = 1 / (x+1) = 2 / 2x + 2

    F(x) = ln |2x+2| + C

    Clearly, f(x) are equal in both cases, but I can't see how ln |2x+2| equals ln |x+1|

    Any explanation? Thanks
    Let u = 2x+2

    therefore du = 2 dx \leftrightarrow dx = \dfrac{du}{2} and \int \dfrac{2}{2x+2} dx = \int \left(\dfrac{2}{u} \cdot \dfrac{du}{2}\right)

    We can cancel those two's to give \int \dfrac{du}{u} and continue as normal from there.
    Last edited by e^(i*pi); July 15th 2011 at 08:25 AM. Reason: fixing missing integral sign
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Siron's Avatar
    Joined
    Jul 2011
    From
    Norway
    Posts
    1,250
    Thanks
    20

    Re: log rule for integration confusion

    If you write: \ln|2x+2|+C=\ln|2(x+1)|+C=\ln(2)+\ln|x+1|+C
    Because \ln(2) is also an constant number you can say:
    \ln|x+1|+C'
    with C' a new constant integration term.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1573
    Awards
    1

    Re: log rule for integration confusion

    Quote Originally Posted by gralla55 View Post
    f(x) = 1 / (x+1), and I want to find it's indefinite integral, I can apply the log rule and get: F(x) = ln |x+1| + C

    F(x) = ln |2x+2| + C
    Clearly, f(x) are equal in both cases, but I can't see how ln |2x+2| equals ln |x+1|
    Your mistake in using the same constant, i.e. they are different constants.

    Recall that \ln(|2x+2|)=\ln(|x+1|)+ln(2).
    If C is the constant in the first then C+\ln(2) is in the second.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Oct 2009
    Posts
    195
    Thanks
    1

    Re: log rule for integration confusion

    Thanks! Now I get it.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Substitution Rule Confusion
    Posted in the Calculus Forum
    Replies: 3
    Last Post: May 17th 2011, 09:19 AM
  2. Integration Confusion
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 22nd 2010, 12:38 AM
  3. help! integration / confusion
    Posted in the Calculus Forum
    Replies: 5
    Last Post: July 23rd 2010, 10:50 PM
  4. Replies: 1
    Last Post: September 27th 2009, 02:12 AM
  5. L'hospital rule confusion
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 16th 2007, 10:36 PM

Search Tags


/mathhelpforum @mathhelpforum