Results 1 to 2 of 2

Math Help - Simple Integral

  1. #1
    Junior Member
    Joined
    Feb 2010
    Posts
    45

    Simple Integral

    So i'm having trouble with a integral that i've been seeing alot lately..It goes like \frac{1}{A+x^2} where A could be anything that is not 1...Now the solution ends up being arctan. However i've been struggling to figure out how to substitute in U to get the right answer...for example \frac{1}{8+x^2} . What should i substitute?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Feb 2010
    Posts
    8
    In the integral

    \int\frac{dx}{{a^2+x^2}}

    By Trigonometric Substitution:

    x=a\tan(\theta),\quad  dx=a\sec^2(\theta)\,d\theta

    \theta=\arctan\left(\frac{x}{a}\right)
    so that the integral becomes

    <br />
\qquad \int\frac{dx}{{a^2+x^2}}
    = [Math]\int\frac{a\sec^2(\theta)\,d\theta}{{a^2+a^2\tan^2 (\theta)}}[/tex]
    = \int\frac{a\sec^2(\theta)\,d\theta}{{a^2(1+\tan^2(  \theta))}}
    = \int \frac{a\sec^2(\theta)\,d\theta}{{a^2\sec^2(\theta)  }}
    = \int \frac{d\theta}{a} = \frac{\theta}{a}+C
    = \frac{1}{a} \arctan \left(\frac{x}{a}\right)+C


    (provided ''a'' > 0).

    The long and short of it is when you have an integral of the form \int\frac{dx}{{a^2+x^2}} you get an result of the form: \frac{1}{a} \arctan \left(\frac{x}{a}\right)+C

    It's a good one to memorize.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Simple way to do an integral
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 12th 2011, 08:02 PM
  2. Simple integral?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 16th 2010, 06:19 AM
  3. Simple Integral Question (I think it's simple)
    Posted in the Calculus Forum
    Replies: 7
    Last Post: February 13th 2010, 03:37 PM
  4. Simple integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 22nd 2009, 06:37 PM
  5. simple integral
    Posted in the Calculus Forum
    Replies: 3
    Last Post: January 7th 2008, 04:47 PM

Search Tags


/mathhelpforum @mathhelpforum