5 once again

Calculus Level 5

0sinx5 dx=1a(b1)Γ(1c)\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 aa, bb, and cc. Submit abcabc.

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

Hint: Use eix=cosx+isinxe^{ix}= \cos{x} + i\sin{x} .

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