Partial fractions with two distinct linear factors

1. A.
   $\ \log\left( \frac{x - 1}{x - 2} \right) + c$, where c is the constant of integration
2. B.
   $\ \log\left( \frac{x - 2}{(x - 1)^{2}} \right) + c$, where c is the constant of integration
3. C.
   $\ \log\left( \frac{x - 2}{x - 1} \right) + c$, where c is the constant of integration
4. D.
   $\log\left( \frac{(x - 2)^{2}}{x - 1} \right) + c$, where c is the constant of integration

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1. A.
   $-5\log|x - 3| + 6\log|x - 4| + c$
2. B.
   $-5\log|x - 3| - 6\log|x - 4| + c$
3. C.
   $5\log|x - 3| - 6\log|x - 4| + c$
4. D.
   $5\log|x - 3| + 6\log|x - 4| + c$

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1. A.
   $\dfrac{8}{5}\log|4 + x| - \dfrac{2}{5}\log|1 - x| + c$
2. B.
   $2\log|4 + x| + \dfrac{2}{5}\log|1 - x| + c$
3. C.
   $-\log|4 + x| + \dfrac{2}{5}\log|1 - x| + c$
4. D.
   $-\dfrac{8}{5}\log|4 + x| - \dfrac{2}{5}\log|1 - x| + c$

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1. A.
   $6$
2. B.
   $7$
3. C.
   $3$
4. D.
   $13$

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1. A.
   $-\dfrac{8}{5}\log|4 - x| - \dfrac{2}{5}\log|1 + x| + c$
2. B.
   $-\dfrac{2}{5}\log|4 + x| - \dfrac{8}{5}\log|1 - x| + c$
3. C.
   $-\dfrac{2}{5}\log|4 - x| - \dfrac{8}{5}\log|1 + x| + c$
4. D.
   $-\dfrac{8}{5}\log|4 + x| - \dfrac{2}{5}\log|1 - x| + c$

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