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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$\displaystyle (a^{2}+1)^{-1}$ is a constant. Integrate a constant and you get ..... . There shouldn't even be an arctan there.
ahh so a is always the constant and x is always the variable. OK, problem solved.
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