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Question Number 70361 by mind is power last updated on 03/Oct/19

Hello   si(x)=−∫_x ^∞ ((sin(x))/x)dx  show ∫_0 ^(+∞) x^(a−1) si(x)dx=−((Γ(a)sin(((πa)/2)))/a)  hint ipp +complex Analysis

$${Hello}\: \\ $$$${si}\left({x}\right)=−\int_{{x}} ^{\infty} \frac{{sin}\left({x}\right)}{{x}}{dx} \\ $$$${show}\:\int_{\mathrm{0}} ^{+\infty} {x}^{{a}−\mathrm{1}} {si}\left({x}\right){dx}=−\frac{\Gamma\left({a}\right){sin}\left(\frac{\pi{a}}{\mathrm{2}}\right)}{{a}} \\ $$$${hint}\:{ipp}\:+{complex}\:{Analysis} \\ $$

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