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Evaluate: intx\ sqrt((1-x)/(1+x))\ dx...

Evaluate: `intx\ sqrt((1-x)/(1+x))\ dx`

Text Solution

Verified by Experts

Given:
`int x sqrt((1-x)/(1+x))\ dx`
`I=int x sqrt((1-x)/(1+x))\ dx`
Let `x= cos 2t implies dx= -2sin2tdt`
`I=int cos2t sqrt((1-cos2t)/(1+cos2t))(-2sin2t)dt`
`I=-2int cos2t sqrt((2cos^2t)/(2sin^2t))sin2tdt`
`I=-2int cos2t (cost)/(sin t)(2sin t cos t)dt`
`I=-2int cos2t (2cos^2t)dt`
...
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