# How do you evaluate the integral #int (2xdx)/(x-1)#?

The integral equals

I would use partial fractions.

Hopefully this helps!

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Another way to see the rewrite.

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To evaluate the integral ∫(2x dx) / (x - 1), you can use the method of partial fraction decomposition. First, rewrite the integrand as 2x / (x - 1). Then, express it as a sum of two fractions with unknown constants A and B: (A / (x - 1)) + (Bx / (x - 1)). Next, find A and B by equating numerators and solving for them. Once you find A and B, integrate each term separately. The integral of A / (x - 1) is A * ln|x - 1|, and the integral of Bx / (x - 1) is B * (x - 1) + C. Finally, combine the results to get the overall integral.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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