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## Main Question or Discussion Point

I am having some difficulty figuring out how to do this integral analytically.

∫r

I have attempted to do integration by parts, but am unable to find any recursion. This would be easy if x was not variable. Also, I have attempted just expanding this term into a Taylor series, but this is not resulting in satisfying results. Any thoughts on how I might approach this one?

tried: u= I

also tried: dv=r*I

∫r

^{1-x}*I_{0}(alpha*r)drI have attempted to do integration by parts, but am unable to find any recursion. This would be easy if x was not variable. Also, I have attempted just expanding this term into a Taylor series, but this is not resulting in satisfying results. Any thoughts on how I might approach this one?

tried: u= I

_{0}(alpha*r) and dv=r^{1-x}also tried: dv=r*I

_{0}(alpha*r) and u= r^{-x}