Integration Help: dx/(5-4x-(x^2))^(5/2)

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SUMMARY

The forum discussion centers on the integration of the function dx/(5-4x-(x^2))^(5/2). The key solution involves completing the square, transforming the expression into 9 - (x + 2)^2. This method simplifies the integration process and can be further aided by substituting y = x + 2, dy = dx. The participants confirm that this approach effectively resolves the integration challenge.

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Homework Statement



Hi everyone
im stuck with the following integration..

Homework Equations



integral of dx/(5-4x-(x^2))^(5/2)

The Attempt at a Solution



can anyone help me?
thanks
 
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… complete the square … !

Hi joseph! :smile:

With quadratics, it's usually best to start by completing the square:

5 - 4x - x^2 = 9 - (x + 2)^2.

(And then you can even change to y = x + 2, dy = dx, if you like!)

Does that help? :smile:
 
OH YEAH!
i never thought of that!
thanks a lot!
 

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