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Evaluate: intx/((1-x^4)^(3/2))dx...

Evaluate: `intx/((1-x^4)^(3/2))dx`

Text Solution

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`I=int frac{x}{(1-x^4)^(3/2)} dx`
`int frac{1}{2(1-u^2)^(3/2)}du` Since `u=x^2`
`1/2 int frac{1}{cos^2v}dv` Since `v=sin^(-1)u`
`1/2tan(sin(-1)(x^2))=1/2frac{x^2}{sqrt(1-x^4)}`
`I=frac{x^2}{2 sqrt(1-x^4)}+C`
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