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Integrate This

  1. Apr 21, 2006 #1
    Find the antiderivative of:


    That's -2x over all of that... Bleh, i suck at code.

    But anyway.. I just started integrals, and this is confusing for me... Is there a product or quotient rule in integrals like there is in derivatives?.. if not? how do you work this?
  2. jcsd
  3. Apr 21, 2006 #2
    Make a substitution, let u = 1-x2 then du = -2x and you have a fairly simple integral in terms of u.
  4. Apr 21, 2006 #3


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    Here is the code for it in case you need to use it in the future (click to see code)

    [tex]\int\frac{-2x}{\sqrt{1-x^2}} \ dx[/tex]
    Last edited: Apr 21, 2006
  5. Apr 21, 2006 #4
    how do you know what to make u and what to make du?
  6. Apr 22, 2006 #5


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    By thinking and analyzing the problem! The difficulty is that [itex]\sqrt{1- x^2}[/itex] in the denominator. The very first thing you should have thought about was substituting for that: u= 1- x^2. Then you would immediately see that du= -2xdx and that would work only if you had an xdx already in the problem (the "-2" is a constant and you can move constants in and out of the integral- you can't do that with "x", the x has to already be there) and, indeed, the problem has an "xdx". Lucky you!

    (Once you've decided what to try for u, you don't "decide" what du is- that follows from the derivative of u. Notice I said "try"- you can seldom look at an integral and know what substitution will work. A lot of it is trial and error.)
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