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int(sin^(-1)x)/(sqrt(1-x^(2)))dx is equa...

`int(sin^(-1)x)/(sqrt(1-x^(2)))dx` is equal to
Where, C is an arbitrary constant.

A

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

B

`(1)/(2)(sin^(-1)x)^(2)+C`

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
B
Let `" "l=int(sin^(-1)x)/(sqrt(1-x^(2)))dx`
Put`" "sin^(-1)x=t" "rArr" "(1)/(sqrt(1-x^(2)))dx=dt`
`therefore" "l=int t dt=(t^(2))/(2)+C=((sin^(-1)x)^(2))/(2)+C`
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