I'm looking for a smart way to define normalized functions. I usually write

```
f[x_] := f[x] = A Sin[x]/x;

```

Then I integrate the function

```
Integrate[f[x], {x, -\[Infinity], \[Infinity]}, Assumptions -> A > 0],

```

take the output and divide f by it

```
g[x_] :=g[x] = f[x]/(A \[Pi]).

```

Is there a better way than this? Thanks