integrate (-1)/(x^2+4)...
i know to pull the negative out...i also know that the derivative of arctanx is 1/1+x^2...where i'm getting confused is factoring the 4 + x^2...the answer to the whole thing is -(1/2)arctan(x/2)+constant...just can't figure out how they got halves when 1/4 seem intuitive...can anyone help?

Question

integrate (-1)/(x^2+4)...
i know to pull the negative out...i also know that the derivative of arctanx is 1/1+x^2...where i'm getting confused is factoring the 4 + x^2...the answer to the whole thing is -(1/2)arctan(x/2)+constant...just can't figure out how they got halves when 1/4 seem intuitive...can anyone help?

anonymous · Answer

Do you know how to evaluate that integral?

$$\Large \int \frac{1}{x^2+1}dx $$

anonymous · Answer

If not we can derive it together, using a trigonometric substitution.

anonymous · Answer

hi...uhm...

anonymous · Answer

just an fyi...when people type in equations on here, all i can see is a bunch of {}//\ etc. I guess this website is supposed to show some nice equation but i can't see them

anonymous · Answer

Oh wow, that's rather impractical *grins*, because as for me, that's one of the main benefits of this website, that things can be LaTeXed out (-: Anyhow let me try a different way, I was talking about this integral:

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