Re: easy integral....

From: Ignacio Larrosa Cañestro (ilarrosaQUITARMAYUSCULAS_at_mundo-r.com)
Date: 09/26/04 

Date: Sun, 26 Sep 2004 18:33:50 +0200

En el mensaje:cj6peo$cu8$1@news.hananet.net,
mina_world <mina_world@hanmail.net> escribió:
> hello...doctor~
>
>
> integral 1 / [sqrt{(x^2) + (a^2)}] dx
>
> ----------------------------------
> x= a tan u (-pi/2 < u < pi/2)
>
> [sqrt{(x^2) + (a^2)}] = a sin u
>
> dx = a (sec u)^2 du
>
> so,
>
> integral 1 / [sqrt{(x^2) + (a^2)}] dx
>
> = integral (1 / [a sin u])*{a (sec u)^2} du
>
> = integral sec u du
>
> = ln |sec u + tan u| + C (this process is omission)
>
> = ln |[sqrt{(x^2) + (a^2)}/a] + [x/a]| + C

It must be

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

An that is

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

 = ln |sqrt{(x^2) + (a^2)} + x| - ln(a) + C

 = ln |sqrt{(x^2) + (a^2)} + x| + C'

with C' = -ln(a) + C 

-- 
Best regards,
Ignacio Larrosa Cañestro
A Coruña (España)
ilarrosaQUITARMAYUSCULAS@mundo-r.com
> ---------------------------------------
> um.....but answer is ln |sqrt{(x^2) + (a^2)} + x| + C
>
> i can't find my error utterly.
>
> help me, please.
>
> thank you very much for your advice.

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