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

[binbagsss]

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

 

[RUber]

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.

 

[binbagsss]

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

 

[RUber]

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.

 

[Mark44]

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.