Re: easy integral....

From: David W. Cantrell (DWCantrell_at_sigmaxi.org)
Date: 09/26/04 

Date: 26 Sep 2004 16:36:09 GMT

"mina_world" <mina_world@hanmail.net> wrote:
> hello...doctor~
>
> integral 1 / [sqrt{(x^2) + (a^2)}] dx

[snip]

> = ln |[sqrt{(x^2) + (a^2)}/a] + [x/a]| + C
>
> ---------------------------------------
> um.....but answer is ln |sqrt{(x^2) + (a^2)} + x| + C
>
> i can't find my error utterly.

They're both correct, differing only but a quantity (depending on the
parameter a) which is constant with respect to x. The latter form is nicer,
however, since it allows us to use a=0.

BTW, let me suggest that you avoid needless grouping symbols. For example,

 ln | sqrt(x^2 + a^2)/a + x/a | + C

is easier to read than your

 ln |[sqrt{(x^2) + (a^2)}/a] + [x/a]| + C.

David

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