# Thread: Trouble identifying K when applying antiderivative rules

1. ## 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

2. 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.

3. 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?