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### Intergral of x/(2x-2) - Two different answers, which one is correct? [duplicate]

I want to find the integral $$\int\frac{x}{2x-2}dx$$ This is just a simple question from my textbook. But there seems to be two ways of solving it. If I simplify it to: $$\int1+\frac{2}{2x-2}dx$$ I ...
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