The purpose of this study is to assess the feasibility of performing a randomized clinical trial evaluating the effect of salpingectomy (removal of the fallopian tubes) during laparoscopic hysterectomy on ovarian function. The hypothesis is that removal of the tubes can prevent diseases of the fallopian tubes such as infection, hydrosalpinx (fluid-filled tubes)and additional invasive procedures such as further imaging work-ups and further surgery related to the tubes.