Results 1 to 3 of 3

Math Help - Evaluating an integral

  1. #1
    Member
    Joined
    Jul 2008
    Posts
    212

    Evaluating an integral

    Evaluate the integral ∫ [x^3/sqrt(x^2+1)] in two different ways.

    a) Integration by parts
    b) The substitution u = sqrt(x^2+1)

    Not sure how to do this, help would be greatly appreciated!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor chisigma's Avatar
    Joined
    Mar 2009
    From
    near Piacenza (Italy)
    Posts
    2,162
    Thanks
    5
    Quote Originally Posted by brumby_3 View Post
    Evaluate the integral ∫ [x^3/sqrt(x^2+1)] in two different ways.

    a) Integration by parts
    b) The substitution u = sqrt(x^2+1)

    Not sure how to do this, help would be greatly appreciated!
    a) by parts...

    ... taking into account the identity...

    (1)

    ... is...



    (2)

    Kind regards

    \chi \sigma
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Mar 2010
    Posts
    715
    Thanks
    2
    Quote Originally Posted by brumby_3 View Post

    b) The substitution u = sqrt(x^2+1)
    \begin{aligned}&  u: = \sqrt{x^2+1} \Rightarrow \frac{du}{dx} = \frac{2x}{2\sqrt{x^2+1}} = \frac{x}{\sqrt{x^2+1}} \Rightarrow dx = \frac{\sqrt{x^2+1}}{x}\;{du} \\& \therefore  \int\frac{x^3}{\sqrt{x^2+1}}\;{dx} = \int\frac{x^3\sqrt{x^2+1}}{x\sqrt{x^2+1}}\;{du} = \int x^2\;{du} = \int (u^2-1)\;{du} = \cdots \end{aligned}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Help evaluating integral
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 12th 2011, 03:23 AM
  2. Evaluating an Integral
    Posted in the Calculus Forum
    Replies: 11
    Last Post: February 26th 2011, 09:07 AM
  3. Evaluating this integral
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 16th 2009, 07:28 PM
  4. help evaluating an integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 11th 2009, 03:23 PM
  5. Replies: 6
    Last Post: May 18th 2008, 07:37 AM

Search Tags


/mathhelpforum @mathhelpforum