the Primitive of$\displaystyle (a^2 + x^2)^-1 = \frac{1}{a} tan^-1(x/a)$

so why does the Primitive of $\displaystyle (a^2 + 1)^-1 = tan^-1(a)$ and not $\displaystyle tan^-1(\frac{1}{a})$?

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- May 15th 2013, 04:24 AMalyosha2Primitive of (a^2 + x^2)^-1
the Primitive of$\displaystyle (a^2 + x^2)^-1 = \frac{1}{a} tan^-1(x/a)$

so why does the Primitive of $\displaystyle (a^2 + 1)^-1 = tan^-1(a)$ and not $\displaystyle tan^-1(\frac{1}{a})$? - May 15th 2013, 04:40 AMBobPRe: Primitive of (a^2 + x^2)^-1
$\displaystyle (a^{2}+1)^{-1}$ is a constant. Integrate a constant and you get ..... . There shouldn't even be an arctan there.

- May 15th 2013, 04:57 AMalyosha2Re: Primitive of (a^2 + x^2)^-1
ahh so a is always the constant and x is always the variable. OK, problem solved.