Integrate This

1. Apr 21, 2006

Jacobpm64

Find the antiderivative of:

-2x
(1-x^2)^(1/2)

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. Apr 21, 2006

d_leet

Make a substitution, let u = 1-x2 then du = -2x and you have a fairly simple integral in terms of u.

3. Apr 21, 2006

dav2008

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

$$\int\frac{-2x}{\sqrt{1-x^2}} \ dx$$

Last edited: Apr 21, 2006
4. Apr 21, 2006

Jacobpm64

how do you know what to make u and what to make du?

5. Apr 22, 2006

HallsofIvy

By thinking and analyzing the problem! The difficulty is that $\sqrt{1- x^2}$ 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.)