If int1/((1+x^(2))sqrt(1-x^(2)))dx=F(x) ...

If `int1/((1+x^(2))sqrt(1-x^(2)))dx=F(x) " and " F(1)=0`,
then for `x gt 0, F(x)=`

A

(a) `1/sqrt(2)tan^(-1)((sqrt(2)x)/sqrt(1+x^(2)))+pi/2`

B

(b) `1/sqrt(2)tan^(-1)((sqrt(2)x)/sqrt(1+x^(2)))-pi/(2sqrt(2))`

C

(c) `1/sqrt(2)tan^(-1)((sqrt(2)x)/sqrt(1-x^(2)))+pi/(2sqrt(2))`

D

(d) `1/sqrt(2)tan^(-1)((sqrt(2)x)/sqrt(1-x^(2)))-pi/(2sqrt(2))`

Verified by Experts

The correct Answer is:

D

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