JEE Advance - Mathematics (1995 - No. 4)

Evaluate the definite integral : $$$\int\limits_{ - 1/\sqrt 3 }^{1/\sqrt 3 } {\left( {{{{x^4}} \over {1 - {x^4}}}} \right){{\cos }^{ - 1}}\left( {{{2x} \over {1 + {x^2}}}} \right)} dx$$$
$$\frac{\pi}{12} \left[ \pi + 3 \log_e(2 + \sqrt{3}) - 4 \sqrt{3} \right]$$
$$\frac{\pi}{6} \left[ \pi + 3 \log_e(2 + \sqrt{3}) - 4 \sqrt{3} \right]$$
$$\frac{\pi}{12} \left[ \pi - 3 \log_e(2 + \sqrt{3}) + 4 \sqrt{3} \right]$$
$$\frac{\pi}{6} \left[ \pi - 3 \log_e(2 + \sqrt{3}) + 4 \sqrt{3} \right]$$
$$\frac{\pi}{24} \left[ \pi + 3 \log_e(2 + \sqrt{3}) - 4 \sqrt{3} \right]$$

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