iterative integration problem

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I'm working on a numerical analysis problem that requires me to find an iterative solution to (1). The resulting integral should take the form (2). However, I cannot figure out what method to use. I first attempted integration by parts, but the most obvious choice of $u = x^n$ and $dv = dx/(x+5)$ results in (3), which isn't what I need. What am I missing?

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