I totally love how the illustrator shows the strain in every muscle group for "leg raised plank".

That's a lot of muscles that will be hurting if you don't work your way up to this advanced planking. 

Good to know.  Good to do.

Plank exercises have a particular effect on our nerves, making them an excellent means of improving overall mood. How? Well, they stretch out muscle groups that contribute to stress and tension in the body. Just think about it: you are sitting in your chair, at home or at work, all day long; your thigh muscles get tight, your legs get heavy due to being bent for several hours; and tension develops in your shoulders due to being forced to slump forward all day. These are all circumstances that put too stress on the muscles and nerves. The good news is that planks not only calm your brain, but they can also treat anxiety and symptoms of depression– but only if you make it part of your daily routine.

Is that true just for plank exercises? Or for all exercises?

Each type of exercise has its own benefit(s) with many overlapping.

I'm looking for the ones that will calm my brain and anxiety. 

Whatever keeps you from ruminating. :)

So... Lifting heavy things.