Compute $ \int\frac{ x}{x-\sqrt{x²+2x+4}}dx$ using Euler substition
I have tried to find the antiderivative of this function :$\frac{ x}{x-\sqrt{x²+2x+4}}$ using the substitution $x=\frac{u^2-4}{2(u+1)}$ for elminate the problem of square root because it is incomplete but really i have got a complicated form , then how do i find : $\displaystyle \int\frac{ x}{x-\sqrt{x²+2x+4}}dx$ by this substitution or if there is any other simple method ?