Evaluating the integral $\int_C |\Bbb dz|/z$

Question

I have to evaluate the integral $$\int_C \frac{|\Bbb dz|}{z}$$ where $C$ is the arc from $z = 1$ to $z = -1-i$. So first of all I made the parameterization $z_1(1-t)+tz_2 = (1-t)x_1+tx_2+i((1-t)y_1+ty_2)$. So I got $1-2t-it$. Then $\Bbb dz = -2\Bbb dt-i\Bbb dt \implies \Bbb dz = (-2-i)$ and $|\Bbb dz| = \sqrt 5 \Bbb dt$. Then I put $$\int \frac{|\Bbb dz|}{z} = \int \frac{\sqrt 5\Bbb dt}{1-2t-it}.$$ And now I just need do integrate. But I’m not sure in previous steps.