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int (dx)/((9+x^(2)))=?...

`int (dx)/((9+x^(2)))=?`

A

`tan^(-1)""(x)/(3)+C`

B

`(1)/(3)tan^(-1)""(x)/(3)+C`

C

` 3tan^(-1)""(x)/(3)+C`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`I=int(dx)/((3^(2)+x^(2)))=(1)/(3)tan^(-1)""(x)/(3)+C.`
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Knowledge Check

  • int(dx)/((1-9x^(2)))=?

    A
    `(1)/(3)log |(1+3x)/(1-3x)|+C`
    B
    `(1)/(3)log |(1-3x)/(1+3x)|+C`
    C
    `(1)/(6)log |(1+3x)/(1-3x)|+C`
    D
    `(1)/(6)log |(1-3x)/(1+3x)|+C`

  • int(dx)/(9x^(2) +1)

    A
    ` (1)/(3) tan^(-1) (2x) + c`
    B
    `(1)/(3) tan^(-1) x + c `
    C
    `(1)/(3) tan^(-1) (3x) + c`
    D
    `(1)/(3) tan^(-1) (6x) + c `

  • int(dx)/((9+4x^(2)))dx=?

    A
    `(1)/(2) tan ^(-1)""(2x)/(3)+C`
    B
    `(1)/(6)tan^(-1)""(2x)/(3)+C`
    C
    `(1)/(6)tan^(-1)""(3x)/(2)+C`
    D
    None of these

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