$\displaystyle \int \frac{x}{\sqrt{1-x^2.(x+\sqrt{1-x^2})^8}}dx$
There seems to be a random dot ( . ) in your equation, indicating a potential typo. Is this supposed to be $\int \frac{x}{\sqrt{(1-x^2)(x + \sqrt{1-x^2})^8}} dx$ or $\int \frac{x}{\sqrt{1-x^2(x + \sqrt{1-x^2})^8}} dx$?