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int((x^2+2))/((x^2+1)(x^2+4))dx (for 0 <...

`int((x^2+2))/((x^2+1)(x^2+4))dx` (for `0 < x < 1)=`

Answer

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Knowledge Check

  • int(5x^2)/((x+1)(x^2+4))dx=

    A
    `log|x+1|+2log|x^2+4|-2tan^(-1)((x)/(2))+c`
    B
    `log|x+1|-2log|x^2+4|+2tan^(-1)((x)/(2))+c`
    C
    `log|x+1|-2log|x^2+4|-2tan^(-1)((x)/(2))+c`
    D
    `log|x+1|+2log|x^2+4|+2tan^(-1)((x)/(2))+c`
  • int(x^(2)+1)/(x^(4)-x^(2)+1)dx=

    A
    `tan^(-1)[(x)/(x^(2)-1)]+c`
    B
    `tan^(-1)[(x^(2)-1)/(x)]+c`
    C
    `-tan^(-1)[(x^(2)-1)/(x)]+c`
    D
    `-cot^(-1)[(x^(2)-1)/(x)]+c`
  • 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`
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