Mathematics

The value of $$\int {\frac{{(1 + {x^2})dx}}{{(1 - {x^2})\sqrt {1 + {x^2} + {x^4}} }}} $$,is


ANSWER

$$ - \frac{1}{{2\sqrt 3 }}{\rm{log}}\left| {\frac{{\sqrt {{x^4} + {x^2} + 1} - \sqrt {3x} }}{{\sqrt {{x^4} + {x^2} + 1} + \sqrt {3x} }}} \right| + C$$

$$\frac{1}{{2\sqrt 3 }}{\rm{log}}\left| {\frac{{\sqrt {{x^4} + {x^2} + 1} + \sqrt {2x} }}{{\sqrt {{x^4} + {x^2} + 1} - \sqrt {2x} }}} \right| + C$$

$$\frac{1}{{2\sqrt 3 }}{\rm{log}}\left| {\frac{{\sqrt {{x^4} - {x^2} + 1} - \sqrt {3x} }}{{\sqrt {{x^4} + {x^2} + 1} + \sqrt {3x} }}} \right| + C$$


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Multiple Correct Medium Published on 17th 09, 2020
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