Solution to an integral problem

[BLUE_CHIP]

Homework Statement

The solution to the integral: $f(r) = \int{ \frac{1}{r} e^{-kr}dr}$

st. $k = const ; k\in ℝ$

Homework Equations

Does this integral have a solution.

The Attempt at a Solution

The obvious method here might be integration by parts this being a product of functions on r. The problem arises in that the exponent does not disappear under differentiation or integration and neither does the 1/r function.

Just affirmation that a solution exists would be sufficient.

Thanks

 

[phyzguy]

The integral exists, but it is not an elementary function. It is called the exponential integral, and is usually abbreviated Ei(x). Here's a link:

http://en.wikipedia.org/wiki/Exponential_integral

 

[dextercioby]

Well, the antiderivative you're looking for may not be expressible in terms of elementary functions, but the its definite integral between 0 and +infinity is a particularly nice number.

 

[BLUE_CHIP]

Thank you very much.