I've just tried to use the Euler's formula for my integral, but I can't get the correct answer. So if anyone could help me I would really appreciate that. This is my integral: $$\int\frac{\sqrt{x^2+2x-1} }{x}\,dx$$
P.S. The ingral must be solven using Euler's formula
This is where I've got stuck: I started with this substitution: $$\sqrt{x^2+2x-1} = -x + t$$ After derivating I get $dx= t^2 + 2x -1 /2(t+1)^2$. After immpleneting it into my integral, I get to this point $$\int\frac{(t^2+2t-1)(t^2+2t-1)}{(t^2+1)2(t+1)^2}\,dt$$ I don't have any idea what I should do next (thought to do another substitution but don't know what to substitute).