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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. $\frac{1}{4 \Gamma(4)}$
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