RE: Integrate and warning messages.

• To: mathgroup at smc.vnet.net
• Subject: [mg35329] RE: [mg35295] Integrate and warning messages.
• From: "DrBob" <majort at cox-internet.com>
• Date: Mon, 8 Jul 2002 03:20:06 -0400 (EDT)
• Reply-to: <drbob at bigfoot.com>
• Sender: owner-wri-mathgroup at wolfram.com

I'm not sure where the equation comes from, but it's an identity, True
for all x:

eqn1 = -Sqrt[1 + 3*x^2]/(1 + Sqrt[1 + 3*x^2]) +
Log[Exp[Sqrt[1 + 3*x^2]]] -
Sqrt[1 + 3*x^2]*(Log[Exp[Sqrt[1 + 3*x^2]]]/(1 + Sqrt[1 + 3*x^2])) ==
0;
eqn2 = Simplify[eqn1 /. 1 + 3*x^2 -> z]
eqn3 = eqn2 /. Sqrt[z] -> y
eqn4 = ((1 + y)*#1 & ) /@ eqn3
eqn5 = (#1 + y & ) /@ eqn4
eqn5 /. Log[E^a_] -> a

(-Sqrt[z] + Log[E^Sqrt[z]])/(1 + Sqrt[z]) == 0
(-y + Log[E^y])/(1 + y) == 0
-y + Log[E^y] == 0
Log[E^y] == y
True

When I say "True for all x", I should omit any x that make denominators
zero in the original equation.  Good luck solving that equation!

Bobby Treat

-----Original Message-----
From: Andrea [mailto:ariciputi at despammed.com]
To: mathgroup at smc.vnet.net
Subject: [mg35329] [mg35295] Integrate and warning messages.

Hi,
I'm trying to solve an integral and before getting the result
Mathematica warns me several times with this message:

Solve::incnst: Inconsistent or redundant transcendental equation.

After reduction, the bad equation is -Sqrt[1+3x^2]/(1+Sqrt[1+3x^2]) +
Log[Exp[Sqrt[1+3x^2]]] - Sqrt[1+3x^2]Log[Exp[Sqrt[1+3x^2]]]/(1+Sqrt[
1+3x^2]) == 0

Can anyone explain it to me??