Curious definite integral : sine integral times exponential

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1. Nov 18, 2014

hmiamid

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 $\mathrm{Si}(x)=\int_0^x \frac{\mathrm{sin}x}{x}\mathrm{d}x$

2. Nov 18, 2014

lgedwards

Integration or differentiation successfully I cleared those paper .!!