Question: Integrating the exponential integral.

Hello everyone,

first, I'd like to mention that I am relatively new to Maple and am therefore thankful for any advice you might have!

I am trying to integrate the term (k_1^2 * r) from a to infinity, see the picture below as well as the attached file. Maple seems to have some issues with that. However, if I break the integral down into more manageable parts it suddenly works! Why is that? How can I get Maple to solve this immeadiately?  I suspect the culprit lies in the term that contains (-Ei(-B*r)*r^(-1)) where Ei is the exponential integral as defined in Maple. The resulting  hypergeometric function seems suspicious.

The problem is that I have to evaluate 21 integrals of this type (k_x*k_y*r) and breaking them down manually becomes pretty cumbersome, especially as the number of terms in the expanded expressions increases. Is there a way to automate this procedure? I guess I would need to extract individual terms and automatically plug them into the integral expression. That should the last resort, however.

The specific problem (everything included for context, weird stuff happens after equation 15):

As for the variables: E, t, and R are real positive numbers. a and B are already assumed as real and positive. A_0, C_0, A_2, and C_2 are real numbers (could be negative, I do not know yet since they must be determined later on). a_0 is definitely real, but it may be negative. r is the polar coordinate, so it is also real and positive, but adding this assumption did not yield a better result.


Thank you for your help!


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