Mathematics

$$\displaystyle\int \frac{x}{\sqrt{\left ( 4-x^{4} \right )}}dx$$


ANSWER

$$\displaystyle \frac{1}{2}\sin ^{-1}\left ( \frac{1}{2}x^{2} \right ).$$


SOLUTION
Let $$\displaystyle I=\int  \frac { x }{ \sqrt { \left( 4-x^{ 4 } \right)  }  } dx$$

Put $$\displaystyle x^{ 2 }=t\Rightarrow 2xdx=dt$$
Therefore
$$\displaystyle I=\frac { 1 }{ 2 } \int  \frac { dt }{ \sqrt { \left( 2^{ 2 }-t^{ 2 } \right)  }  } =\frac { 1 }{ 2 } \sin ^{ -1 } \frac { t }{ 2 } =\frac { 1 }{ 2 } \sin ^{ -1 } \frac { { x }^{ 2 } }{ 2 } $$
Hence, option 'C' is correct.
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Single Correct Medium Published on 17th 09, 2020
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