\[\large \int_0^\infty \sin{x^{5}} \ dx = \frac 1a \left(\sqrt b-1\right) \Gamma \left(\frac 1c \right) \]

The equation above holds true for positive integers \(a\), \(b\), and \(c\). Submit \(abc\).

**Notation:** \(\Gamma(\cdot) \) denotes the gamma function.

**Hint:** Use \(e^{ix}= \cos{x} + i\sin{x} \).

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