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int(x)/(sqrt(1-x^(2)))dx=?...

`int(x)/(sqrt(1-x^(2)))dx=?`

A

`sin^(-1)x+C`

B

`sin^(-1)sqrt(x)+C`

C

`sqrt(1-x^(2))+C`

D

`-sqrt(1-x^(2))+C`

Text Solution

Verified by Experts

The correct Answer is:
D
Put `(1-x^(2))=t and-2xdx=dt`.
`:." "I=-(1)/(2)intdt=-(1)/(2)intt^((-1)/(2))dt=-(1)/(2)*(sqrt(t))/(((1)/(2)))+C=-sqrt(t)+C`.
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