Integral quick q , integrate ((1-x)/(1+x))^1/2

In summary, the conversation discusses the best method for integrating ##(\frac{1-x}{1+x})^{\frac{1}{2}} ##, with suggestions of multiplying by 1 and using trigonometric substitution to solve the integral. The use of partial fractions is dismissed as it is not applicable to the given function.
  • #1
binbagsss
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Homework Statement



How do I go about integrating
##(\frac{1-x}{1+x})^{\frac{1}{2}} ##?

Homework Equations


above

The Attempt at a Solution


im not really sure.
could integrate by partial fractions if it was to the power of ##1##, only thing i can think of

thanks in advance
 
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  • #2
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.
 
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  • #3
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.

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
 
  • #4
I'm not sure if my definition of partial fractions is the same as yours, but
##\int \frac{1}{\sqrt{1 -x^2} }\, dx ## and ##\int \frac{x}{\sqrt{1 -x^2}} \, dx## both have known integrals.
 
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  • #5
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
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.

Trig substitution is definitely the way to go after applying @RUber's suggestion.
 

1. What is the purpose of integrating the function ((1-x)/(1+x))^1/2?

The purpose of integrating this function is to find the area under the curve of the function. This can help in calculating the total change or accumulation of a certain quantity over a given interval.

2. How do you solve for the integral of ((1-x)/(1+x))^1/2?

To solve for the integral, you can use the substitution method. Let u = 1+x, which means du = dx. Then, the integral becomes ∫((1-x)/u)^1/2 du. This can be simplified using the power rule and solved using basic integration techniques.

3. What are the limits of integration for this integral?

The limits of integration for this integral will depend on the given interval. If the interval is not specified, the limits can be from -∞ to +∞.

4. Is there a shortcut or formula for solving this type of integral?

Yes, there is a shortcut known as the trigonometric substitution method. This involves substituting u = tanθ and using trigonometric identities to simplify the integral. However, it is important to understand the underlying concept and principles of integration before using shortcuts.

5. Can this integral be solved using a calculator or software?

Yes, most scientific calculators and software programs have built-in integration functions that can solve this integral. However, it is always recommended to understand the steps and process of solving integrals manually before relying on technology.

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