Results 1 to 2 of 2

Math Help - integration with trig substitution

  1. #1
    Member
    Joined
    Jan 2009
    Posts
    91

    integration with trig substitution

    integrate:

    2x^2 / x^2 + 4 dx


    how do know which substitution to use here and what happens to the numerator???
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,519
    Thanks
    1404
    Quote Originally Posted by razorfever View Post
    integrate:

    2x^2 / x^2 + 4 dx


    how do know which substitution to use here and what happens to the numerator???
    First do some long division to turn the integrand into

    2 - \frac{8}{x^2 + 4}.


    Then you work with the fact that \int{\frac{1}{a^2 + x^2}\,dx} = \frac{1}{a}\arctan{\left ( \frac{x}{a} \right )} + C.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Integration with Trig. Substitution
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 19th 2010, 05:04 PM
  2. Integration by Trig Substitution
    Posted in the Calculus Forum
    Replies: 4
    Last Post: March 17th 2010, 10:06 PM
  3. Integration by Trig substitution
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 11th 2010, 03:32 AM
  4. Integration by trig substitution
    Posted in the Calculus Forum
    Replies: 4
    Last Post: March 8th 2009, 12:52 AM
  5. Integration by trig substitution
    Posted in the Calculus Forum
    Replies: 3
    Last Post: June 4th 2008, 01:19 PM

Search Tags


/mathhelpforum @mathhelpforum