I am solving a problem that involves the following integral:
$$ \int_x^\infty \frac{e^{-t}}{t^2} dt $$
According to WolframAlpha, for the real part of x being positive, this is equivalent to:
$$ \int_x^∞ \frac{e^{-t}}{t^2} dt = \frac{e^{-x}}{x} - Γ(0, x) $$
I do not understand how to incorporate the gamma function/exponential integral as this is defined as the following, with a factor of $\frac{1}{t}$ instead of $\frac{1}{t^2}$:
$$ Γ(0, x) = E_1(x) = \int_x^\infty \frac{e^{-t}}{t} dt$$
I'd understand if the difference doesn't matter for t approaching infinity, as the limit of the integrand is 0 anyway, but I'd like to know if I am missing some other connection here.