Confused about these derivations from the appendix page 15 of paper https://link.springer.com/article/10.1007/s11071-019-05117-z
bit I can't follow is in the picture here:
dot denotes differentiation w.r.t to $t$ and dash denotes differentiation w.r.t to $s$ (arc length).
Says by using by parts, but the first derivation is for a multivariable function so it is a bit different? Tried to use standard by parts but can't seem to get anywhere.
Also, the presence of a discontinuity in the system complicates the integrals more denoted by the $\xi$ terms. Thanks very much.