Mathematics

$$\displaystyle \int \frac{x\: dx}{1+x^{4}}$$ is equal to


ANSWER

$$\displaystyle \frac{1}{2}\tan ^{-1}x^{2}+k$$


SOLUTION
$$\displaystyle \int \dfrac{x\: dx}{1+x^{4}}$$

$$\displaystyle =\int  \dfrac { x\: dx }{ 1+{ (x }^{ 2 })^{ 2 } } $$

Put $${ x }^{ 2 }=t$$
$$\Rightarrow 2xdx=dt$$

$$\displaystyle =\dfrac { 1 }{ 2 } \int  \dfrac { dt }{ 1+t^{ 2 } } $$

$$\displaystyle =\dfrac { 1 }{ 2 } \tan ^{ -1 }{ t } +k$$

$$I=\displaystyle \dfrac{1}{2}\tan ^{-1}x^{2}+k$$
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Single Correct Medium Published on 17th 09, 2020
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