If you're taking two derivatives you can add a constant and something linear in t.

如果你要二次求导,你可以添加一个一次项和常数项

耶鲁公开课 - 基础物理课程节选

If you're taking only one derivative you can add a constant.

如果只进行一次求导,你可以添加一个常数项

耶鲁公开课 - 基础物理课程节选

Normally I couldn't do that Vdp because this term would have p dV plus V dp, but we've specified the pressure is constant, so the dp part is zero.

一般情况下我不能这么写,因为这一项会包含pdV和，但是我们已经假定压强为常数，所以包含dp的部分等于零。

麻省理工公开课 - 热力学与动力学课程节选

You'll put time t=0, x doesn't have this term, doesn't have this term, and it is c.

你令时间t=0,这一项就消失了,这一项也是,只剩下常数c

耶鲁公开课 - 基础物理课程节选