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∫0∞sinx5 dx=1a(b−1)Γ(1c)\large \int_0^\infty \sin{x^{5}} \ dx = \frac 1a \left(\sqrt b-1\right) \Gamma \left(\frac 1c \right) ∫0∞sinx5 dx=a1(b−1)Γ(c1)
The equation above holds true for positive integers aaa, bbb, and ccc. Submit abcabcabc.
Notation: Γ(⋅)\Gamma(\cdot) Γ(⋅) denotes the gamma function.
Hint: Use eix=cosx+isinxe^{ix}= \cos{x} + i\sin{x} eix=cosx+isinx.
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