X-FeedAbuse: http://nntpfeed.proxad.net/abuse.pl feeded by 82.66.60.35
Path: ...!news.mixmin.net!proxad.net!feeder1-2.proxad.net!nntpfeed.proxad.net!pasdenom.info!from-devjntp
Message-ID: <yhA5iWwD5PniE5mU18P1MXO61IE@jntp>
JNTP-Route: news2.nemoweb.net
JNTP-DataType: Article
Subject: Re: Intregation
References: <86A71or-P6OBYR6Lk52cGepvYN8@jntp> <t46910$l2b$1@gioia.aioe.org>
Newsgroups: fr.sci.maths
JNTP-HashClient: pA7UcErMAecwOTZr7LRpaBeN7pA
JNTP-ThreadID: 3y6x6Sv6dSIYSpHqNx6RWuLBm_8
JNTP-Uri: http://news2.nemoweb.net/?DataID=yhA5iWwD5PniE5mU18P1MXO61IE@jntp
User-Agent: Nemo/0.999a
JNTP-OriginServer: news2.nemoweb.net
Date: Mon, 25 Apr 22 16:10:32 +0000
Organization: Nemoweb
JNTP-Browser: Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/100.0.4896.127 Safari/537.36
Injection-Info: news2.nemoweb.net; posting-host="a082d72449e6c2691f4dc2ddc972fd99f35fa04a"; logging-data="2022-04-25T16:10:32Z/6839385"; posting-account="4@news2.nemoweb.net"; mail-complaints-to="newsmaster@news2.nemoweb.net"
JNTP-ProtocolVersion: 0.21.1
JNTP-Server: PhpNemoServer/0.94.5
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
X-JNTP-JsonNewsGateway: 0.96
From: Richard Hachel <r.hachel@tiscali.fr>
Bytes: 1913
Lines: 20

Le 25/04/2022 à 15:51, Samuel DEVULDER a écrit :
> Le 25/04/2022 à 14:01, Richard Hachel a écrit :
>> How integrate
>> ∫ sqrt (1+x²)
> 
> Tu veux la primitive de √(1+x²) ou la primitive de l'intégrale ?
> 
> Dans le 1er cas, c'est simple
> https://www.wolframalpha.com/input?i=antiderivative+of+sqrt+%281%2Bx%C2%B2%29+
> 
> 1/2 (√(x² + 1) x + sinh⁻¹(x)) + constant

Un autre internaute me répond.

= 1/2 (x Sqrt[1 + x^2] + ArcSinh[x])

Mais ça reste assez compliqué.

R.H.