#JavaScript (ES6), <s>33</s> <s>28</s> 23 bytes

<!-- language-all: lang-js -->

    (n,x=n)=>--x?n*f(n,x):n

Add 7 bytes if we need to allow for negative integers.

    (n,x=n>0?n:-n)=>--x?n*f(n,x):n

And add 3 bytes if `0` should be output for input `0`

    (n,x=n>0?n:-n)=>n&&--x?n*f(n,x):n

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##Try It

<!-- begin snippet: js hide: false console: true babel: false -->

<!-- language: lang-js -->

    f=
    (n,x=n)=>--x?n*f(n,x):n
    o.innerText=f(i.value=3)
    i.oninput=_=>o.innerText=f(+i.value)

<!-- language: lang-html -->

    <input id=i min=0 type=number><pre id=o>

<!-- end snippet -->

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##History
###28 bytes
    n=>eval(1+("*"+n).repeat(n))
###33 bytes
    n=>eval(Array(n).fill(n).join`*`)