The discussion revolves around the integration of the expression \((\frac{1-x}{1+x})^{\frac{1}{2}}\). Participants are exploring various methods and considerations related to this integral.
Participants are actively discussing different approaches, including the potential use of trigonometric substitution and the limitations of partial fraction decomposition for the given integral. There is no explicit consensus, but several productive lines of reasoning are being explored.
There are indications that participants are grappling with the definitions and applicability of certain mathematical techniques, such as partial fractions and trigonometric integrals, in the context of the problem.
RUber said:What if you multiplied by 1,
i.e.
## 1= \frac{\sqrt{1-x}}{\sqrt{1-x}}##
Then you might have something that looks like a known integral using trig functions.
Partial fractions isn't appropriate here, either. Assuming you could break up ##(\frac{1-x}{1-x^2})^{1/2}## into ##(\frac{A}{1-x} + \frac B {1 + x})^{1/2}##, you still have the sum of the two fractions being raised to the 1/2 power.binbagsss] How do I go about integrating ##(\frac{1-x}{1+x})^{\frac{1}{2}} ##? [h2]The Attempt at a Solution[/h2] im not really sure. could integrate by partial fractions if it was to the power of ##1## said:oh thanks, so by doing that I get ##\int \frac{1-x}{(1-x^{2})^{1/2}} dx ##, which I can partial fraction and then integrate