When accelerating between 30 and 40 the whole car starts vibrating really bad. If I let of the gas it stops. Sometimes when it is put in drive or reverse there is a clanking noise but most of the time it's really smooth.

Have the drive axles checked for worn inner cv joints.

i agree with pushrod, its a driveline issue, check the c/v axles and the u-joint on the driveshaft, either way if you've had the car for a while, or bought it from someone who didn't seem to keep regular maintenance i'd have these parts replaced.