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Evaluate: int1/((1+sqrt(x))sqrt(x-x^2))d...

Evaluate: `int1/((1+sqrt(x))sqrt(x-x^2))dx`

Text Solution

Verified by Experts

Given I=`int1/((1+sqrt(x))sqrt(x-x^2))dx`
`(1+sqrt(x))`=t
then,`1/2sqrt(x)dx=dt`
I=`int 2dt/((t)sqrt(2t-t^2))`
Again put `t=1/z`⇒`dt=−1​/z^2 dz`
⇒`I=2∫(−1​/z^2 dz)/((1/z)​sqrt(2/z−1/z^2))​ `
​=`−2sqrt(2z−1 ...
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