Partial fractions with a repeated linear factor, such as 1/((x - a)^2 (x - b))

1. A.
   $-\dfrac{5}{9}\log(x+1)+\dfrac{5}{9}\log(x-2)-\dfrac{4}{3}\cdot\dfrac{1}{x-2}+C$
2. B.
   $-\dfrac{5}{9}\log(x+1)+\dfrac{5}{9}\log(x-2)-\dfrac{1}{x-2}+C$
3. C.
   $\dfrac{1}{9}\log(x+1)+\dfrac{5}{9}\log(x-2)-\dfrac{4}{3}\cdot\dfrac{1}{x-2}+C$
4. D.
   $-\dfrac{5}{9}\log(x+1)+\dfrac{1}{9}\log(x-2)-\dfrac{1}{x-2}+C$

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1. A.
   $\frac{2}{9}\log(x-1)+\frac{1}{3}\times\frac{1}{x-1}+\frac{2}{9}\log(x+2)+c$
2. B.
   $\frac{2}{9}\log(x-1)-\frac{1}{3}\times\frac{1}{(x-1)}+\frac{2}{9}\log(x+2)+c$
3. C.
   $\frac{2}{9}\log(x-1)+\frac{1}{3}\times\frac{1}{x-1}-\frac{2}{9}\log(x+2)+c$
4. D.
   $\frac{2}{9}\log(x-1)-\frac{1}{3}\times\frac{1}{x-1}-\frac{2}{9}\log(x+2)+c$

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1. A.
   $-\dfrac{1}{2x^2} + \dfrac{1}{x} + \log\left|\dfrac{x}{x + 1}\right| + c$
2. B.
   $\dfrac{1}{2x^2} + \dfrac{1}{x} + \log\left|\dfrac{x}{x + 1}\right| + c$
3. C.
   $-\dfrac{1}{2x^2} - \dfrac{1}{x} + \log\left|\dfrac{x}{x + 1}\right| + c$
4. D.
   $-\dfrac{1}{2x^2} - \dfrac{1}{x} - \log\left|\dfrac{x}{x + 1}\right| + c$

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