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Unformatted text preview: dx . This is easy enough to get however. Just solve the substitution for x as follows, Using this substitution the integral is now, So, sometimes, when an integral contains the root the substitution, can be used to simplify the integral into a form that we can deal with. Lets take a look at another example real quick. Example 2 Evaluate the following integral. Solution Well do the same thing we did in the previous example. Heres the substitution and the extra work well need to do to get x in terms of u . With this substitution the integral is, This integral can now be done with partial fractions. Setting numerators equal gives, Picking value of u gives the coefficients. The integral is then, So, weve seen a nice method to eliminate roots from the integral and put into a form that we can deal with. Note however, that this wont always work and sometimes the new integral will be just as difficult to do....
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 Fall '08
 prellis
 Integrals

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