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Evaluate: intsqrtx/(a^3-x^3)\ dx...

Evaluate: `intsqrtx/(a^3-x^3)\ dx`

Text Solution

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I= `intsqrtx/(a^3-x^3)\ dx`
I=`intsqrtx/((a^(3/2))^2-(x^(3/2))^2)\ dx`
let,
`x^(3/2)=t`
`3/2x^(1/2)dx=dt`
`x^(1/2)dx=2/3dt`
`I=2/3intsqrtx/((a^(3/2))^2-t^2)\ dx`
`I=2/3sin^(-1)(t/(a^(3/2)))+C`
...
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