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

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

Text Solution

Verified by Experts

Let, `1-x^2=t^2`
`-xdx=tdt`

`x^2=1-t^2`

`1+x^2=2-t^2`

`=int1/((1+x^2)sqrt(1-x^2))\ dx`

`=int(-tdt)/((2-t^2)t)`

`=int(dt)/((t^2-2))`

`=(1)/(2sqrt(2))ln((t-sqrt(2))/(t+sqrt(2)))`

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