That is correct

You have the wrong limits of integration, the integral should be from v=u to 1For the marginal density of v, I did the the integral of 1/u with respect to u and I got ln(u). I then plugged in 0 and 1 and I got 0. For the ln u, when I plugged in the 0, I just did the limit as u approaches 0 and that is zero. So it should be 0-0, which is zero.

CB