Integral confusion
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From: Jon Joseph on 7 Feb 2010 06:15 All: Is this integral wrong? If not could someone explain the minus sign inside the log? Integrate[1/(x + 1) - 1/(x + 6), x] // Simplify log(-2 (x + 1)) - log(2 (x + 6)) Thanks, Jon.=
From: Peter Breitfeld on 8 Feb 2010 03:32 Jon Joseph wrote: > All: Is this integral wrong? If not could someone explain the minus sign > inside the log? > > Integrate[1/(x + 1) - 1/(x + 6), x] // Simplify > > log(-2 (x + 1)) - log(2 (x + 6)) > > Thanks, Jon.= > No, it's not wrong, because if you take the derivative of the result you get your integrand back. It only differs from the result you get by calculating the integral "by hand" by the constant log(-2)-log(2), so it is a valid "stammfunktion" (German, how do you call that in English? antiderivative?) -- _________________________________________________________________ Peter Breitfeld, Bad Saulgau, Germany -- http://www.pBreitfeld.de
From: Tony Harker on 8 Feb 2010 03:33 It's not wrong: remember there's an arbitrary constant of integration, so you can rewrite the result in terms of the Log[x+1] and Log[x+6] that you were probably expecting. Tony ]-> -----Original Message----- ]-> From: Jon Joseph [mailto:josco.jon(a)gmail.com] ]-> Sent: 07 February 2010 11:13 ]-> To: mathgroup(a)smc.vnet.net ]-> Subject: Integral confusion ]-> ]-> All: Is this integral wrong? If not could someone explain ]-> the minus sign ]-> inside the log? ]-> ]-> Integrate[1/(x + 1) - 1/(x + 6), x] // Simplify ]-> ]-> log(-2 (x + 1)) - log(2 (x + 6)) ]-> ]-> Thanks, Jon.= ]-> ]->
From: Gregory Duncan on 8 Feb 2010 03:33 I get Log[1 + x] - Log[6 + x] which is also apparent from observation. On Sun, Feb 7, 2010 at 3:12 AM, Jon Joseph <josco.jon(a)gmail.com> wrote: > All: Is this integral wrong? If not could someone explain the minus sign > inside the log? > > Integrate[1/(x + 1) - 1/(x + 6), x] // Simplify > > log(-2 (x + 1)) - log(2 (x + 6)) > > Thanks, Jon.= > >
From: Leonid Shifrin on 8 Feb 2010 03:34
Hi Jon, I get the same result (M7). Looks like a bug. Regards, Leonid On Sun, Feb 7, 2010 at 3:12 AM, Jon Joseph <josco.jon(a)gmail.com> wrote: > All: Is this integral wrong? If not could someone explain the minus sign > inside the log? > > Integrate[1/(x + 1) - 1/(x + 6), x] // Simplify > > log(-2 (x + 1)) - log(2 (x + 6)) > > Thanks, Jon.= > > |