I want to solve:
$$\int\frac{1}{1+\frac{2}{x}-x} \mathrm{d}x $$
I don't know how to start, maybe I should use partial fraction?
2026-04-05 20:17:16.1775420236
Finding $\int \frac{\mathrm{d}x}{1 + \frac{2}{x} - x}$
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Multiply by $\frac{x}{x}$ to get a more recognisable form $$\int \frac{x}{2 + x - x^2} \, \mathrm{d}x = \int \frac{-x}{(x+1)(x-2)} \, \mathrm{d}x$$
Some partial fractions (I'll leave the gory details to you) yields $$-\frac{1}{3}\int \frac{1}{x+1} + \frac{2}{x-2} \, \mathrm{d}x$$
which are easy logarithmic anti-derivatives.