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int(dx)/(sqrt(8+2x-x^(2)))...

`int(dx)/(sqrt(8+2x-x^(2)))`

A

`(1)/(3)sin^(-1) ((x-1)/(3))+c`

B

`sin^(-1)((x+1)/(3))+C`

C

`(1)/(3)sin^(-1) ((x+1)/(3))+c`

D

`sin^(-1)((x-1)/(3))+c`

Text Solution

Verified by Experts

The correct Answer is:
D
`int (dx)/(sqrt(8+2x-x^(2))=int (dx)/(sqrt((8-(x^(2)-2x+1)+1))`
`int (dx)/(sqrt(3^(2)-(x-1)^(2))=sin^(-1) ((x-1)/(3))+c`
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