Results 1 to 3 of 3
Like Tree2Thanks
  • 2 Post By Prove It

Math Help - int x/(x^2+1)

  1. #1
    Boo
    Boo is offline
    Junior Member
    Joined
    Jan 2013
    From
    Pizza
    Posts
    57

    int x/(x^2+1)

    hello!

    I have to solve :
    \int \frac{x}{x^2+1}dx=\frac{1}{2}ln|x^2+1|+C

    well: \int \frac{x}{x^2+1}dx=\frac{1}{2}\int\frac{2xdx}{x^2+1  }

    if weknow that:
    \int u^{-1}du=\int \frac{1}{u}du and u=x^2+1

    then what do we exactly do with 2xdx in the numerator? Dont we just have 2x too much???

    many thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,402
    Thanks
    1291

    Re: int x/(x^2+1)

    It's because when you substitute \displaystyle \begin{align*} u = x^2 + 1 \end{align*}, that means \displaystyle \begin{align*} \frac{du}{dx} = 2x \end{align*}. So

    \displaystyle \begin{align*} \int{\frac{x}{x^2 + 1}\,dx} &= \frac{1}{2}\int{ \frac{1}{x^2 + 1}\cdot 2x \, dx} \\ &= \frac{1}{2} \int{ \frac{1}{u} \, \frac{du}{dx} \, dx } \\ &= \frac{1}{2}\int{ \frac{1}{u}\,du} \end{align*}

    which you can now integrate.
    Thanks from Boo and topsquark
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Boo
    Boo is offline
    Junior Member
    Joined
    Jan 2013
    From
    Pizza
    Posts
    57

    Re: int x/(x^2+1)

    Thanks!
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum