Results 1 to 8 of 8

Math Help - How to calculate int(ln(x)/(x+1))?

  1. #1
    Member
    Joined
    May 2007
    Posts
    237

    How to calculate int(ln(x)/(x+1))?

    Does anybody know how to calculate the integral  \int{\frac{lnx}{1+x}} ? Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by curvature View Post
    Does anybody know how to calculate the integral  \int{\frac{lnx}{1+x}} ? Thanks.
    I don't think it can be expressed using a finite number of elementary functions. Perhaps it's meant to be a definite integral ....?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,408
    Thanks
    1294
    Quote Originally Posted by curvature View Post
    Does anybody know how to calculate the integral  \int{\frac{lnx}{1+x}} ? Thanks.
    According to Mathematica,

    \int{\frac{\ln{x}}{1 + x}\,dx} = \ln{x}\ln{(1 + x)} + \textrm{Li}_2(-x)

    where \textrm{Li}_2(-x) = \sum_{k = 1}^{\infty}{\frac{(-x)^k}{k^2}}

    This is the Polylogarithm function, see Polylogarithm - Wikipedia, the free encyclopedia.

    I do not know how it is calculated to be this function though...
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    May 2007
    Posts
    237
    Quote Originally Posted by mr fantastic View Post
    I don't think it can be expressed using a finite number of elementary functions. Perhaps it's meant to be a definite integral ....?
    I mean an indefinite integral.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by curvature View Post
    I mean an indefinite integral.
    Are you looking for an answer like the one in post #3?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    May 2007
    Posts
    237
    Quote Originally Posted by mr fantastic View Post
    Are you looking for an answer like the one in post #3?
    Perhaps post#3 offers the best answer since I no concise form is possible to the integral.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,408
    Thanks
    1294
    Quote Originally Posted by curvature View Post
    Perhaps post#3 offers the best answer since I no concise form is possible to the integral.
    Are you sure you copied down the integral correctly?

    \int{\frac{\ln{x}}{x + 1}\,dx} is hard, but

    \int{\frac{\ln{x}}{x}\,dx} is easy, you just use a u-substitution...
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Member
    Joined
    May 2007
    Posts
    237
    Quote Originally Posted by Prove It View Post
    Are you sure you copied down the integral correctly?

    \int{\frac{\ln{x}}{x + 1}\,dx} is hard, but

    \int{\frac{\ln{x}}{x}\,dx} is easy, you just use a u-substitution...
    I mean the first one. Thank you.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Is it possible to calculate x and y....
    Posted in the Algebra Forum
    Replies: 2
    Last Post: November 29th 2010, 01:16 PM
  2. calculate
    Posted in the Algebra Forum
    Replies: 5
    Last Post: April 27th 2010, 09:35 AM
  3. Calculate
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 14th 2010, 02:11 AM
  4. Calculate M4
    Posted in the Calculus Forum
    Replies: 5
    Last Post: March 29th 2010, 08:44 PM
  5. Calculate this sum
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: August 28th 2009, 11:50 PM

Search Tags


/mathhelpforum @mathhelpforum