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Math Help - Trouble identifying K when applying antiderivative rules

  1. #1
    Junior Member
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    Sep 2010
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    Trouble identifying K when applying antiderivative rules

    So I have two questions where I cannot find apply the antiderivative rule properly.

    Q1

    g(x) = 1/ 9(x^2 + 1)

    The rule is 1 / (1+k^2 * x^2) = 1/k * tan^-1 * kx + C

    I get 1/9 * tan^-1 * 9x + C

    The answer for somereaso does not have a 9 in front of the x for the tan. How come? Isn't the K = 9 ?

    Q2

    Same problem except the question is 1 / 1+ 36x^2 and I get 1/36 * tan^-1 36x + C


    Please help.
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  2. #2
    Senior Member
    Joined
    Mar 2010
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    You have
    \int \frac{dx}{1+k^2x^2}=\frac{1}{k}tan^{-1}(kx)+C

    You want
    \int \frac{dx}{1+36x^2}=\int \frac{dx}{1+6^2x^2}
    there k=6 (not 36 !)

    \int \frac{dx}{9(1+x^2)}=\frac{1}{9}\int \frac{dx}{1+x^2}
    What k is in this case?

    Or you want this
    \int \frac{dx}{9x^2+1} \: \: ?
    Please find k in this case.
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  3. #3
    Junior Member
    Joined
    Sep 2010
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    K should be 3 in that case.

    Apparently I've been using k in a form where it's squared but I cannot see that at first glance. I mean, I know 36 is the 6^2 but say for example it was 41 instead of 36. Is there a reason why when the number can be square rooted we take that instead of the number given?
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