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int (x+ ( cos^(-1)3x )^(2))/(sqrt(1-9x ^...

`int (x+ ( cos^(-1)3x )^(2))/(sqrt(1-9x ^(2)))dx = (1)/(k _(1)) ( sqrt(1-9x ^(2))+ (cos ^(-1) 3x )^(k_(2)))+c, ` then `k _(1) ^(2)+k_(2)^(2)=` (where C is an arbitrary constnat. )

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Knowledge Check

  • If int (2^(x))/(sqrt(1-4^(x))) dx = k sin ^(-1) (f(x)) + C then :

    A
    ` k = log 2, f(x) = 2^(x)`
    B
    `k = (1)/(log 2) , f(x) = 2^(x)`
    C
    `k = log 2, f(x) = 4^(x)`
    D
    `k = (1)/(log2) , f(x) = 4^(x)`

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