Let $f\left(x\right)=7{\tan }^{8}x+7{\tan }^{6}x-3{\tan }^{4}x-3{\tan }^{2}x$ for all $x\in \left(-\frac{\pi }{2},\frac{\pi }{2}\right).$ Then the correct expression(S) is(are)

• Correct answer
  A

  $\underset{0}{\overset{\frac{\pi }{4}}{\int }}x f\left(x\right)dx=\frac{1}{12}$
• Correct answer
  B

  $\underset{0}{\overset{\frac{\pi }{4}}{\int }} f\left(x\right)dx=0$
• C

  $\underset{0}{\overset{\frac{\pi }{4}}{\int }}x f\left(x\right)dx=\frac{1}{6}$
• D

  $\underset{0}{\overset{\frac{\pi }{4}}{\int }}x f\left(x\right)dx=1$

Hence, the correct answer is options: 'A', 'B'.