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Everybody,

I need to solve a definite integral of exponential integral function combined with exponentials and rational functions, which is presented as follows:

$\int\limits_a^\infty {z\exp \left( { - \left( {b - c} \right)z} \right){\rm{Ei}}\left( { - cz} \right)} dz$

where $a, b, c >0$ are constants, and $\text{Ei}(z)$ is the exponential integral function defined as $${\rm{Ei}}\left( z \right) = \int\limits_{ - \infty }^z {\frac{{\exp \left( t \right)}}{t}dt}$$

If this integral can not be solved, any approximation is welcomed as well.

Thanks a lot for your reading and help!

graydad
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junxv penn
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  • ${\rm{Ei}}\left( z \right)$ is the exponential integral function, defined as ${\rm{Ei}}\left( z \right) = \int\limits_{ - \infty }^z {\frac{{\exp \left( t \right)}}{t}dt} $ – junxv penn Jul 13 '15 at 03:05
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    Welcome to Mathematics Stack Exchange ! I think that it could be good you explain what you already tried and tell where you are stuck. By the way, the antiderivative exists. – Claude Leibovici Jul 13 '15 at 07:59
  • Thanks for your answer! Claude. – junxv penn Jul 15 '15 at 04:53

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