Partial fractions in x^2 for (x^2 + a)(x^2 + b) denominators (put x^2 = t)

1. A.
   $\frac{9}{14}\tan^{-1}\!\frac{x}{2}+\frac{5}{14\sqrt{3}}\log\left|\frac{x-\sqrt{3}}{x+\sqrt{3}}\right|+c$
2. B.
   $\frac{9}{7}\tan^{-1}\!\frac{x}{2}+\frac{5}{7\sqrt{3}}\log\left|\frac{x-\sqrt{3}}{x+\sqrt{3}}\right|+c$
3. C.
   $\frac{9}{7}\tan^{-1}\!\frac{x}{2}-\frac{5}{7\sqrt{3}}\log\left|\frac{x-\sqrt{3}}{x+\sqrt{3}}\right|+c$
4. D.
   $\frac{9}{14}\tan^{-1}\!\frac{x}{2}+\frac{5}{7}\log\left|\frac{x-\sqrt{3}}{x+\sqrt{3}}\right|+c$

Tap an option to check your answer.

1. A.
   $\frac{1}{12}$
2. B.
   $\frac{21}{12}$
3. C.
   $\frac{- 1}{12}$
4. D.
   $\frac{- 21}{12}$

Tap an option to check your answer.

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

Tap an option to check your answer.

1. A.
   $-\left(\dfrac{\sqrt{2}}{3}\tan^{-1}\dfrac{x}{\sqrt{2}} + \dfrac{\sqrt{5}}{3}\tan^{-1}\dfrac{x}{\sqrt{5}}\right) + c$, where c is the constant of integration
2. B.
   $\left(\dfrac{\sqrt{2}}{3}\tan^{-1}\dfrac{x}{\sqrt{2}} + \dfrac{\sqrt{5}}{3}\tan^{-1}\dfrac{x}{\sqrt{5}}\right) + c$, where c is the constant of integration
3. C.
   $\dfrac{\sqrt{2}}{3}\tan^{-1}\left(\dfrac{x}{\sqrt{2}}\right) - \dfrac{\sqrt{5}}{3}\tan^{-1}\left(\dfrac{x}{\sqrt{5}}\right) + c$, where c is the constant of integration
4. D.
   $-\dfrac{\sqrt{2}}{3}\tan^{-1}\left(\dfrac{x}{\sqrt{2}}\right) + \dfrac{\sqrt{5}}{3}\tan^{-1}\left(\dfrac{x}{\sqrt{5}}\right) + c$, where c is the constant of integration

Tap an option to check your answer.