\( \int \frac{x d x}{x^{4}+x^{2}+1} \) equals (a) \( \frac{2}{3} \t...

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Counter-Strike: Source
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Counter-Strike: Source (2004)
Duration: 2:48
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\( \int \frac{x d x}{x^{4}+x^{2}+1} \) equals
(a) \( \frac{2}{3} \tan ^{-1}\left(\frac{2 x^{2}+1}{\sqrt{3}}\right)+C \)
(b) \( \frac{1}{\sqrt{3}}\left[\tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)-\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)\right]+C \)
(c) \( \frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{2 x^{2}+1}{\sqrt{3}}\right)+C \)
(d) \( \frac{1}{\sqrt{3}}\left[\tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)+\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)\right]+C \) where \( C \) is an arbitrary constant.
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