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int (x^(2))/(x^(4)-x^(2)-12)dx...

`int (x^(2))/(x^(4)-x^(2)-12)dx`

Text Solution

Verified by Experts

The correct Answer is:
`1=(1)/(7)log|(x-2)/(x+2)|+(sqrt(3))/(7) tan^(-1) ((x)/(sqrt(3)))+C`
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Knowledge Check

  • int(x^(2)+1)/(x^(4)-x^(2)+1)dx=...+c

    A
    `x tan^(-1) ((x^(2)+1)/(x))`
    B
    `tan^(-1)((x^(2)-1)/(x))`
    C
    `(1)/(sqrt(2)) tan^(-1)((x^(2)+1)/(sqrt(2x)))`
    D
    `(1)/(sqrt(2)) tan^(-1)((x^(2)-1)/(sqrt(2x)))`

  • Integration by partial fraction : int(x^(2)-1)/(x^(4)+x^(2)+1)dx=...

    A
    `(1)/(2)log((x^(2)+x+1)/(x^(2)-x+1))+c`
    B
    `(1)/(2)log((x^(2)-x-1)/(x^(2)+x+1))+c`
    C
    `log((x^(2)-x+1)/(x^(2)+x+1))+c`
    D
    `(1)/(2)log((x^(2)-x+1)/(x^(2)+x+1))+c`

  • int(x^(2)+1)/(x(x^(2)-1))dx=....

    A
    `"log"(x^(2)-1)/(x)+c`
    B
    `-"log"(x^(2)-1)/(x)+c`
    C
    `"log"(x)/(x^(2)+1)+c`
    D
    `-"log"(x)/(x^(2)+1)+c`

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