As shown in the figure, let the chain mass be m and the length be l, take the lowest point as the origin, establish the Y axis upward, and designate the lowest point as the potential energy point 0.

Take the infinitesimal dy at the coordinate y, and the infinitesimal mass dm=(m/L)dy.

Trace element gravitational potential energy? DV= dmgy= (mg/l) ydy

What about the whole gravitational potential energy chain?

V=∫dV=(mg/L)∫ydy？

Substitute the upper limit of integral l? Is the lower limit 0 integral available? V=mgL/2