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int(xsin^(-1)x^(2))/(sqrt(1-x^(4)))dx...

`int(xsin^(-1)x^(2))/(sqrt(1-x^(4)))dx`

Text Solution

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`=int x^{n} d x=frac{x^{n+1}}{n+1}+c`
Therefore,
` Put sin ^{-1} x^{2}=t`
` Rightarrow frac{1}{sqrt{1-(x^{2})^{2}}} times 2 x times d x=d t `
` Rightarrow frac{2 x}{sqrt{1-x^{4}}} d x=d t `
` int t(frac{d t}{2})=frac{1}{2} int t d t=frac{t^{2}}{4}+c `
` ...
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