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int (x^2+2x+4)/((x+1)sqrt(x^2+1)) dx...

`int (x^2+2x+4)/((x+1)sqrt(x^2+1)) dx`

Answer

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(i) int (dx)/(x sqrt(x^2-1)) (ii) int (dx)/(x sqrt(ax -x^2))

int(1)/((x-1)sqrt(x^(2)+4))dx

Knowledge Check

  • int(x^2-1)/(x^3sqrt(2x^4-2x^2+1)) dx is equal to :

    A
    `(sqrt(2x^4-2x^2+1))/(x(x^2-1))+c`
    B
    `(sqrt(2x^4-2x^2+1))/(x^3)+c`
    C
    `(sqrt(2x^4-2x^2+1))/(x^2)+c`
    D
    `(sqrt(2x^4-2x^2+1))/(2x^2)+c`
  • int(x^4-1)/(x^2sqrt(x^4+x^2+1))dx =

    A
    `sqrt(x^2+1/x^2+1)`
    B
    `(sqrt(x^4+x^2+1))/x`
    C
    `sqrt((x^4+x^2+1)/x)`
    D
    none of these
  • int1/((x-1)sqrt(x^(2)-4))dx=

    A
    `-1/sqrt(5)logabs(1/(x-1)+1/5+sqrt((x^(2)+4)/(x-1)^(2)))+c`
    B
    `-1/sqrt(5)logabs(1/(x-1)+1/5+sqrt((x^(2)+4)/(5(x-1)^(2))))+c`
    C
    `-1/sqrt(5)logabs(1/(x-1)+1/5sqrt((x^(2)+4)/(x-1)^(2)))+c`
    D
    None of these
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