Why k mustn't be equal to 1 to use this formula? $int1/sqrt(x^2 + k) = ln|x + sqrt(x^2 + k)|$

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Answer 1 · 2018-05-15T08:01:41

$"k can be equal to 1 without a problem"$

$"If we derive the RHS for k = 1 we get LHS as should :"$

$(1 + (2x)/(2 sqrt(x^2 + k)))/(x + sqrt(x^2 + k))$

$= ((2 sqrt(x^2 + k) + 2x)/(2 sqrt(x^2 + k)))/(x + sqrt(x^2+k))$

$= ((sqrt(x^2 + k) + x)/sqrt(x^2 + k))/(x + sqrt(x^2 + k))$

$= 1 / sqrt(x^2 + k)$

Why k mustn't be equal to 1 to use this formula? int1/sqrt(x^2 + k) = ln|x + sqrt(x^2 + k)|int1/sqrt(x^2 + k) = ln|x + sqrt(x^2 + k)|