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0-sinx-x-1-a-dx-




Question Number 142256 by rs4089 last updated on 28/May/21
∫_0 ^∞ ((sinx)/x^(1−a) )dx
0sinxx1adx
Answered by Dwaipayan Shikari last updated on 28/May/21
∫_0 ^∞ ((sin (x))/x^μ )dx=(π/(2Γ(μ)sin((μ/2)π)))  ∫_0 ^∞ ((sin (x))/x^(1−a) )=(π/(2Γ(1−a)cos(a(π/2))))
0sin(x)xμdx=π2Γ(μ)sin(μ2π)0sin(x)x1a=π2Γ(1a)cos(aπ2)

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