hmiamid
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Hello, and thanks for welcoming me in the forum of Physics Forums.
I just found a curious integral that I solved by Taylor series. I wondered if it comes from a bigger group of integral definitions:
##\int_0^\infty \mathrm{Si}(ax)e^{-x}\mathrm{d}x=\mathrm{atan}(a)##
Where Si(x) is the sine integral function ##\mathrm{Si}(x)=\int_0^x \frac{\mathrm{sin}x}{x}\mathrm{d}x##
I just found a curious integral that I solved by Taylor series. I wondered if it comes from a bigger group of integral definitions:
##\int_0^\infty \mathrm{Si}(ax)e^{-x}\mathrm{d}x=\mathrm{atan}(a)##
Where Si(x) is the sine integral function ##\mathrm{Si}(x)=\int_0^x \frac{\mathrm{sin}x}{x}\mathrm{d}x##