Results 1 to 6 of 6

Math Help - Basic integral problem.

  1. #1
    Newbie
    Joined
    Mar 2008
    Posts
    8

    Basic integral problem.

    Is the answer to integrate x/x+3dx this:

    ln|x+3|+c ????
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Lord of certain Rings
    Isomorphism's Avatar
    Joined
    Dec 2007
    From
    IISc, Bangalore
    Posts
    1,465
    Thanks
    6
    Quote Originally Posted by navynukejones View Post
    Is the answer to integrate x/x+3dx this:

    ln|x+3|+c ????
    No it is,
    \int \frac{x}{x+3} \, dx = \int (1 - \frac{3}{x+3}) \, dx = x - 3\ln|x+3| + C
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2008
    Posts
    8

    Are you sure?

    I think you have to use the formula: the integral of du/u = ln|u|+C and in this problem u=x+3 and therefore du=dx.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member disclaimer's Avatar
    Joined
    Dec 2007
    Posts
    77
    Quote Originally Posted by navynukejones View Post
    I think you have to use the formula: the integral of du/u = ln|u|+C and in this problem u=x+3 and therefore du=dx.
    It works only when the numerator is the derivative of the denominator, eg. \int{\frac{dx}{x+3}}=\ln|x+3|+C
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Lord of certain Rings
    Isomorphism's Avatar
    Joined
    Dec 2007
    From
    IISc, Bangalore
    Posts
    1,465
    Thanks
    6
    Quote Originally Posted by navynukejones View Post
    I think you have to use the formula: the integral of du/u = ln|u|+C and in this problem u=x+3 and therefore du=dx.

    Just observe carefully.... there is a x term in the numerator. So according to you u = x+3, du = dx.

    So \int \frac{x}{x+3} \, dx = \int \frac{x}{u} \, du

    But hey you have to get rid of that x in the above expression
    Thats why write \frac{x}{x+3} = 1 - \frac{3}{x+3}. Both the terms now are easily integrable
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by navynukejones View Post
    Is the answer to integrate x/x+3dx this:

    ln|x+3|+c ????
    Ok..just to let you know... \int\frac{x}{x+c}dx=\int\frac{x+c-c}{x+c}dx=\int\frac{x+c}{x+c}dx-\int\frac{c}{x+c}dx =x-c\ln|x+c|+C
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. (Basic) Integral
    Posted in the Calculus Forum
    Replies: 10
    Last Post: May 30th 2011, 09:44 PM
  2. integral , basic ..
    Posted in the Math Challenge Problems Forum
    Replies: 6
    Last Post: January 9th 2010, 01:56 AM
  3. help with basic integral problem?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 2nd 2009, 07:20 PM
  4. Replies: 2
    Last Post: September 5th 2009, 04:24 PM
  5. very basic integral
    Posted in the Calculus Forum
    Replies: 11
    Last Post: June 30th 2009, 07:10 PM

Search Tags


/mathhelpforum @mathhelpforum