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I was reading about the Risch Algorithm on Wikipedia, and came across the example below, which was taken from Bronstein's "Symbolic Integration Tutorial". I do not currently have access to this textbook.

The relatively simple form of the answer intrigued me, but I've not been able to compute the integrand yet.

$$ \int \dfrac{(x+1)^2 + (3x+1) \sqrt{x + \ln x}}{x \sqrt{x + \ln x}(x + \sqrt{x + \ln x})} \, dx = 2(\sqrt{x + \ln x} + \ln{( x + \sqrt{x + \ln x})}) + C $$

How can one evaluate this?

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  • $\begingroup$ A PDF can be found here $\endgroup$ – user170231 Jan 18 '15 at 3:56

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