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int(1/sqrt(9-25x^2)) dx...

`int(1/sqrt(9-25x^2))` dx

A

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

B

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

C

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

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`int(dx)/(sqrt(9-25x^(2)))=int(dx)/(sqrt(25[((3)/(5))^(2)-x^(2)]))=(1)/(5)int(dx)/(sqrt([((3)/(5))^(2)-x^(2)]))`
`=(1)/(5)sin^(-1)((x)/(3//5))+C`
`=(1)/(5)sin^(-1)((5x)/(3))+C`
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