* Could you help to integrate

dE = (m+dm)*v*dv + (c^2)*dm

I would like to compare the result with relativistic kinetic energy

which as you know is calculated by equation

E = mc^2( 1/(1-v^2/c^2)^(1/2) -1 )

Kinetic energy - Wikipedia, the free encyclopedia

Thank you very much for any possible help.