Integrating the Square Root of a Fraction: How to Solve This Tricky Integral

[alialice]

Homework Statement

$\int \sqrt {\frac{1+x}{1-x}} dx =$ ?

The solution is:

$= \arcsin{x} -\sqrt{1-x^2} + const$

If someone could help me to find the solution I'll be very pleased! :-)
Thanks everybody!

 

[phosgene]

Try multiplying the integrand by $\frac{\sqrt{1+x}}{\sqrt{1+x}}$ and remember that $(1+x)(1-x) = 1 - x^2$. If you consider what the derivative of $arcsin(x)$ is, it's easier to see what you should be trying to do to the integral. You may also need to do a substitution.