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int 1/ sqrt (a^2 + x^2) dx = log ( x + s...

`int 1/ sqrt (a^2 + x^2) dx = log ( x + sqrt(x^2 + a^2)) + c`

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int log(x+sqrt(x^(2)+a^(2)))dx

int(1)/(sqrt(x^(2)-a^(2)))=log(x+sqrt(x^(2)-a^(2)))

Knowledge Check

  • int_(-a)^(a) log (x+ sqrt(x^(2) + 1 ) ) dx

    A
    `2 log (a^(2) +1)`
    B
    `2 log ( sqrt(a^(2) +1) -a)`
    C
    `0`
    D
    `2 log ( a+ sqrt(a^(2) + 1) )`

  • "If "int (1)/(sqrt(4x^(2)-5))dx=alpha log|x+sqrt(x^(2)-beta)|,"then "alpha+2beta is

    A
    `-2`
    B
    2
    C
    `-3`
    D
    `3

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