I agree with the other guys, that you won't be able to straighten out that bulged case. Now having said that...If Ray had told ME that straightening MY 37mm case was IMPOSSIBLE, I would suffer a serious attack of contrarianism and be driven to search my metal scrap box for a piece of round stock about five or six inches long (12 to 15cm) and slightly wider than the base of the projectile. I would chuck the round stock into my little Chinese toy metal lathe and turn down about two and a half inches (6.5cm) to the same diameter as the projectile base, so that the casing is a snug fit on it. Then I would part off a disc about a quarter of an inch thick. Back to the stock in the lathe-center drill it about an inch and a half (38mm) deep and tap the resulting hole to a convenient size, then part off a threaded disc about an inch (25mm) long. I have a 3/4 inch x16 tap at hand so That is what I would use, even though I will probably have to make a trip to the ranch and feed store to get an appropriate bolt. For anyone reading this from a metric speaking country, use whatever you have handy, but I think that bigger is better in this case.
Now look down in the bottom of the case. Does the wall of the primer pocket protrude into the powder cavity? I thought so. We are going to put a lot of pressure on the bottom of the case and it will deform the base if it is all concentrated on the primer protrusion. We need a piece of hardwood dowel turned down to fit through the case mouth and with a divot drilled out for the primer protrusion. Length isn't critical, but it should sit below the bulge when inserted into the case.
We need to anneal the bulged brass. That means heating it with a propane torch until it just barely glows red in a darkened room. Now remember that piece of turned round stock that is still chucked in the lathe? Force the shell onto this mandrel and turn the lathe on really slow. Now apply the propane torch to the bulged area until it barely starts to glow. Don't overcook the brass, it will be ruined if you burn it. When the bulge just barely glows red, turn off the torch and probably the lathe too. You can quench the case in water or just let it cool slowly. It might be a good idea to practice annealing on some of the more common cartridge cases that you have stashed under your work bench.
It would be nice to know the original length of the cartridge case so that we don't stretch it to the point where we wildcat a new 37mm cartridge or, even worse, rip the case neck from the shoulder. Somebody help us out here. OK, we are ready to do this. Place the wooden dowel in the cartridge case with the divot over the primer pocket protrusion. Place the thin steel disc over the wood dowel to keep the bolt from driving itself into the dowel. Apply SUPERGLUE to the periphery of threaded disc and insert it squarely into the case mouth so that the top of the disk is flush with the case mouth. You might want to practice this without the superglue a couple of times. The bolt can be used to force the threaded disc back out. Allow the superglue to set up for however long the instructions indicate. Once the glue has set, screw the bolt into the threaded hole until it bottoms out. Now give the bolt two or three turns with a wrench. Did the bulge go away a little? I sure hope so. Now here is where I tell you that you are on your own. Continue stretching the case until it is close to the original length. How much more you stretch it is up to you, but I don't think that this method will remove the bulge completely.When you are satisfied, turn out the bolt so that it makes a good handle and apply the propane torch to the threaded disc and the case neck where they are glued together. The superglue will release at 400 to 450 degrees F. Wiggle the bolt until the threaded disc starts to move and then pull it out. It will be hot so gloves would be good. If the superglue fails to hold, I would use soft solder, but the glue is easier to clean off the of the brass.
I doubt that the case neck will be perfectly smooth. There are a couple methods that might be used to further smooth things out. Have you ever heard of metal spinning? Neither have I, but U-Tube has some interesting metal spinning videos. I would probably try to make a ring die that approximates the original shoulder. I wouldn't try to force this die under pressure, but I would twist it down over the case neck to try and burnish away any remaining ripples.
Don't forget to wear your eye protection.