Cool Puzzle! I had never seen these before.
Final Solution:
![enter image description here](https://cdn.statically.io/img/i.sstatic.net/0OOiT.png)
Step 1:
![enter image description here](https://cdn.statically.io/img/i.sstatic.net/MV3DF.png)
The tile must extend out. It cannot connect to the next shaded cell because it would be size 6. It cannot block off the unshaded cells, so it must therefor be the F tile.
Step 2:
![enter image description here](https://cdn.statically.io/img/i.sstatic.net/ojsgq.png)
This is the only cell that is not a border and has no adjacent unshaded cells. It must be the X tile
Step 3:
![enter image description here](https://cdn.statically.io/img/i.sstatic.net/AmKb4.png)
Through extension and allowing the unshaded to attach, the top left is forced to U tile
Step 4:
![enter image description here](https://cdn.statically.io/img/i.sstatic.net/SoCFn.png)
L tile is forced through extension and connection
Step 5:
![enter image description here](https://cdn.statically.io/img/i.sstatic.net/06bTU.png)
N tile is forced through extension and connection
Step 6:
![enter image description here](https://cdn.statically.io/img/i.sstatic.net/4VgsP.png)
This is the only location that the I tile fits.
Step 7:
![enter image description here](https://cdn.statically.io/img/i.sstatic.net/KeEkJ.png)
All possibilities for tiles that fit in this location other than P were already used.
Step 8:
![enter image description here](https://cdn.statically.io/img/i.sstatic.net/ikvKI.png)
With P used, that leaves only T for the bottom left corner.
Step 9:
![enter image description here](https://cdn.statically.io/img/i.sstatic.net/QCgAN.png)
Through extension and connection, only Z fits in the bottom middle
Step 10:
![enter image description here](https://cdn.statically.io/img/i.sstatic.net/JYIlL.png)
Through extension and connection, W is the only tile that fits on the left.
Step 11:
![enter image description here](https://cdn.statically.io/img/i.sstatic.net/VIZ16.png)
The unshaded cell to the right and up blocked the V tile, so the Y tile is the only one that fits
Step 12:
![enter image description here](https://cdn.statically.io/img/i.sstatic.net/MUSrQ.png)
There are two possible orientations for the V tile. One blocks off half of the puzzle and prevents connection, therefore only one orientation remains to solve the puzzle.