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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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I'm currently operating with the following integral: $$\int\frac{u'(t)}{(1-u(t))^2} dt$$ But I notice that $$\frac{d}{dt} \frac{u(t)}{1-u(t)} = \frac{u'(t)}{(1-u(t))^2}$$ and $$\frac{d}{dt} \frac{... 3answers 4k views ### Two different solutions to integral Given the very simple integral $$\int -\frac{1}{2x} dx$$ The obvious solution is \int -\frac{1}{2x} dx = -\frac{1}{2} \int \frac{1}{x} dx = -\frac{1}{2} ... 3answers 454 views ### Which of these answers is the correct indefinite integral? (Using trig-substitution or u-substitution give different answers) Answers obtained from two online integral calculators:$$\begin{align}\int\dfrac{\sqrt{1 + x}}{\sqrt{1 - x}}\,\mathrm dx &= -\sqrt{\dfrac{x + 1}{1 - x}} + \sqrt{\dfrac{x + 1}{1 - x}}x - 2\...

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