Partial fractions with a linear and an irreducible quadratic factor

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

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1. A.
   $\frac{5}{4}$
2. B.
   $- \frac{5}{4}$
3. C.
   $- \frac{5}{3}$
4. D.
   $\ - \frac{5}{6}$

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1. A.
   $\dfrac{1}{5}\log|x + 2| - \dfrac{1}{10}\log(x^2 + 1) + \dfrac{2}{5}\tan^{-1}x + C$
2. B.
   $\log|x + 2| + \dfrac{1}{10}\log(x^2 + 1) + \dfrac{1}{5}\tan^{-1}x + C$
3. C.
   $5\log|x + 2| + 10\log(x^2 + 1) + \tan^{-1}x + C$
4. D.
   $\log|x + 2| + \dfrac{1}{10}\log(x^2 + 1) - \dfrac{1}{5}\tan^{-1}x + C$

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