If you want to convert acceleration to velocity, etc., cumtrapz() in matlab is probably what you want (this is second order trapezoidal integration). The only catch is that if you are integrating real vibration data, there is almost certainly a small DC offset. No matter how good your AC coupling is, it is not perfect. There will be a tiny non-zero offset at 0 Hz. When integrated, this becomes huge in the output signal. Therefore you will almost certainly need to high pass filter your data after integration.
