



 
Matt, I think what you want to find is the antiderivative or sometimes called the integral of 1/(x(1  x)), not the derivative. I would do exactly what you did, write 1/(x(1  x)) = 1/x + 1/(1  x) and find the antiderivative of 1/x and 1/(1  x) separately. Integration is somewhat of an art that relies on your experience and knowledge of what functions you can already integrate. When I see 1/(x(1  x)) i recognize that I can integrate a constant divided by x and also a constant divided by (1  x) so I wonder "Can I write 1/[x(1  x)] = a/x + b/(1  x) for some constants a and b?"
I hope this helps,  


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