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Evaluate: int1/(sqrt(16-6x-x^2))\ dx...

Evaluate: `int1/(sqrt(16-6x-x^2))\ dx`

A

`sin^(-1)((x-3)/(5))+C`

B

`sin^(-1)((x+3)/(5))+C`

C

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

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`(16-6x-x^(2))=[-(x^(2)+6x+9)+25]={25-(x+3)^(2)}`
`therefore I=int(dx)/sqrt(5^(2)-(x+3)^(2))=int(dt)/(sqrt(5^(2)-t^(2)))=sin^(-1)""(t)/(5)+C=sin^(-1)((x+3)/(5))+C.`
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