Consider the function $f(x)$ defined as $f(x)=c e^{-x^{4}}, x \in \mathbb{R}$
For what value of $c$ is $f$ a probability density function?
1. $\frac{2}{\Gamma(1 / 4)}$
2. $\frac{4}{\Gamma(1 / 4)}$
3. $\frac{3}{\Gamma(1 / 3)}$
4. $\frac{1}{4 \Gamma(4)}$