Results 1 to 3 of 3

Math Help - Integration - Algebraic substitution

  1. #1
    Senior Member
    Joined
    Jul 2006
    From
    Shabu City
    Posts
    381

    Integration - Algebraic substitution

    \int \frac{dx}{\sqrt{2x} - \sqrt {x+4}}

    what will i substitute?

    let z^2 = x + 4
    x = z^2 - 4
    dx = 2zdz

    but its no use
    i will get a result of

    \int \frac{2zdz}{\sqrt{z^2-4}-z}
    need help pls
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,666
    Thanks
    298
    Awards
    1
    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    \int \frac{dx}{\sqrt{2x} - \sqrt {x+4}}

    what will i substitute?

    let z^2 = x + 4
    x = z^2 - 4
    dx = 2zdz

    but its no use
    i will get a result of

    \int \frac{2zdz}{\sqrt{z^2-4}-z}
    need help pls
    Start by rationalizing the denominator of the integrand:
    \int \frac{dx}{\sqrt{2x} - \sqrt {x+4}} = \int \frac{dx}{\sqrt{2x} - \sqrt {x+4}} \cdot \frac{\sqrt{2x} + \sqrt{x + 4}}{\sqrt{2x} + \sqrt{x + 4}} = \int \frac{\sqrt{2x} + \sqrt{x + 4}}{2x - (x + 4)} dx

    = \int \frac{\sqrt{2x} + \sqrt{x + 4}}{x - 4} dx

    Now split the integrand into two terms and see what you can do with it.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Jul 2006
    From
    Shabu City
    Posts
    381
    got it now thanks ts!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Algebraic Substitution Calculator
    Posted in the Math Software Forum
    Replies: 1
    Last Post: March 22nd 2011, 11:26 AM
  2. Integration by substitution
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 3rd 2009, 08:14 PM
  3. algebraic/trigonometric substitution
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 6th 2007, 09:25 AM
  4. Integration - Algebraic substitution
    Posted in the Calculus Forum
    Replies: 2
    Last Post: July 31st 2007, 05:44 AM
  5. Replies: 1
    Last Post: July 12th 2007, 03:52 PM

Search Tags


/mathhelpforum @mathhelpforum