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

1 Answer
MattyMatty
May 15, 2018

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

Explanation:

#"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)#

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