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.