Integral $\int_{1}^{2011} \frac{\sqrt{x}}{\sqrt{2012 - x} + \sqrt{x}}dx$ Evaluate:
$$\int_{1}^{2011} \frac{\sqrt{x}}{\sqrt{2012 - x} + \sqrt{x}}dx$$
Using real methods only.
I am not sure what to do.
I tried finding a power series, which was too ugly.
I just need some hints, not an answer to do this integral, this is from the MIT Integration bee 2012.

HINT:
As $\displaystyle\int_a^bf(x)\ dx=\int_a^bf(a+b-x)\ dx$
So, if $\int_a^bf(x)\ dx=I,$
$$2I=\int_a^b[f(x)+f(a+b-x)]\ dx$$
