damped harmonic oscillator, urgent help needed!
Homework Statement
for distinct roots (k1, k2) of the equation k^2 + 2Bk + w^2 show that x(t) = Ae^(k1t) + Be^(k2t) is a solution of the following differential equation: (d^2)x/dt^2 + 2B(dx/dt) + (w^2)x = 0
Homework Equations
The...
Homework Statement
Show that the definite integral from 0 to 1 (ln x)^n dx = n!(-1)^n
Homework Equations
The Attempt at a Solution
i tried to integrate by parts and kept going on and on but i don't know how to incorporate the factorial in the answer ...