RE: [obm-l] Ajuda - Integral

["Paulo Santa Rita" <p_ssr@xxxxxxxxxxx>]

Ola Wallace,

Use o Maple :
int((1+((a^2 + x^2)^(1/2)))/(1 - ((a^2 + x^2)^(1/2))), x ) ;

O resultado e grande e dificil de escrever de forma legivel aqui. Veja :

-2/(-1+a^2)^(1/2)*arctan(x/(-1+a^2)^(1/2))-1/(-(a-1)*(a+1))^(1/2)*((x-(-(a-1)*(a+1))^(1/2))^2+2*(-(a-1)*(a+1))^(1/2)*(x-(-(a-1)*(a+1))^(1/2))+1)^(1/2)-ln(x+((x-(-(a-1)*(a+1))^(1/2))^2+2*(-(a-1)*(a+1))^(1/2)*(x-(-(a-1)*(a+1))^(1/2))+1)^(1/2))+1/(-(a-1)*(a+1))^(1/2)*arctanh(1/2*(2+2*(-(a-1)*(a+1))^(1/2)*(x-(-(a-1)*(a+1))^(1/2)))/((x-(-(a-1)*(a+1))^(1/2))^2+2*(-(a-1)*(a+1))^(1/2)*(x-(-(a-1)*(a+1))^(1/2))+1)^(1/2))+1/(-(a-1)*(a+1))^(1/2)*((x+(-(a-1)*(a+1))^(1/2))^2-2*(-(a-1)*(a+1))^(1/2)*(x+(-(a-1)*(a+1))^(1/2))+1)^(1/2)-ln(x+((x+(-(a-1)*(a+1))^(1/2))^2-2*(-(a-1)*(a+1))^(1/2)*(x+(-(a-1)*(a+1))^(1/2))+1)^(1/2))-1/(-(a-1)*(a+1))^(1/2)*arctanh(1/2*(2-2*(-(a-1)*(a+1))^(1/2)*(x+(-(a-1)*(a+1))^(1/2)))/((x+(-(a-1)*(a+1))^(1/2))^2-2*(-(a-1)*(a+1))^(1/2)*(x+(-(a-1)*(a+1))^(1/2))+1)^(1/2))-x

Um Abraco
Paulo Santa Rita
4,1420,230604

>From: "Wallace Martins" <wallace@poli.ufrj.br>
>Reply-To: obm-l@mat.puc-rio.br
>To: obm-l@mat.puc-rio.br
>Subject: [obm-l] Ajuda - Integral
>Date: Wed, 23 Jun 2004 13:03:20 -0300
>
>Ola,
>alguem poderia me ajudar com esta integral indefinida (esta dando muita 
>conta)?
>
>Integral{[1 + (x^2 + a^2)^(1/2)]/[1 - (x^2 + a^2)^(1/2)]}
>
>Wallace
>LPS/UFRJ

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