Primitive of (a^2 + x^2)^-1

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May 15th 2013, 04:24 AM
alyosha2

Primitive of (a^2 + x^2)^-1

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

so why does the Primitive of $(a^2 + 1)^-1 = tan^-1(a)$ and not $tan^-1(\frac{1}{a})$ ?
May 15th 2013, 04:40 AM
BobP

Re: Primitive of (a^2 + x^2)^-1

$(a^{2}+1)^{-1}$ is a constant. Integrate a constant and you get ..... . There shouldn't even be an arctan there.
May 15th 2013, 04:57 AM
alyosha2

Re: Primitive of (a^2 + x^2)^-1

ahh so a is always the constant and x is always the variable. OK, problem solved.

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