Question Number 142256 by rs4089 last updated on 28/May/21
$$\int_{\mathrm{0}} ^{\infty} \frac{{sinx}}{{x}^{\mathrm{1}−{a}} }{dx} \\ $$
Answered by Dwaipayan Shikari last updated on 28/May/21
$$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{sin}\:\left({x}\right)}{{x}^{\mu} }{dx}=\frac{\pi}{\mathrm{2}\Gamma\left(\mu\right){sin}\left(\frac{\mu}{\mathrm{2}}\pi\right)} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{sin}\:\left({x}\right)}{{x}^{\mathrm{1}−{a}} }=\frac{\pi}{\mathrm{2}\Gamma\left(\mathrm{1}−{a}\right){cos}\left({a}\frac{\pi}{\mathrm{2}}\right)} \\ $$