JEE Advance - Mathematics (2004 - No. 9)
Find the value of $$\int\limits_{ - \pi /3}^{\pi /3} {{{\pi + 4{x^3}} \over {2 - \cos \left( {\left| x \right| + {\pi \over 3}} \right)}}dx} $$
$$\frac{4\pi}{\sqrt{3}}\left[\tan^{-1}(3) - \frac{\pi}{4}\right]$$
$$\frac{2\pi}{\sqrt{3}}\left[\tan^{-1}(3) - \frac{\pi}{4}\right]$$
$$\frac{4\pi}{\sqrt{3}}\left[\tan^{-1}(3) + \frac{\pi}{4}\right]$$
$$\frac{\pi}{\sqrt{3}}\left[\tan^{-1}(3) - \frac{\pi}{4}\right]$$
$$\frac{4\pi}{3}\left[\tan^{-1}(\sqrt{3}) - \frac{\pi}{4}\right]$$
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