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Evaluate: int(x^2)/(sqrt(1-x ))dx...

Evaluate: `int(x^2)/(sqrt(1-x ))dx`

Text Solution

Verified by Experts

Given: `int(x^2)/(sqrt(1-x ))dx`
`I=int(x^2)/(sqrt(1-x ))dx`
Let` x=sin^2t implies dx=2sin t cos tdt`
`I=int (sin^4t)/(sqrt(1-sin^2t)) 2sin t cos t dt `
`I=int (sin^4t)/(cost)) 2sin t cos t dt `
`I=int (sin^4t)2sin t dt `
`I=2int (1-cos^2t)^2 sin t dt `
Now let `cos t=u implies -sintdt=du`
...
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