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I am trying to solve the next integral, using this method of rational functions.

My problem is, that I turn the function into two expressions with the same denominator...when I try to use values of x, I will always make zero of both sides, if you know what I mean

\[\int \frac{x+1}{(x-4)^{2}}dx=\int (\frac{A}{x-4}+\frac{B}{x-4})dx\]

I'll be happy to see an example how to solve such integrals.

Thank you !