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MathGroup Archive 2007

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Re: Integrate

  • To: mathgroup at smc.vnet.net
  • Subject: [mg74057] Re: Integrate
  • From: "Jean-Marc Gulliet" <jeanmarc.gulliet at gmail.com>
  • Date: Thu, 8 Mar 2007 04:33:21 -0500 (EST)
  • References: <esls78$q0v$1@smc.vnet.net> <45EE98F8.8010107@gmail.com>

On 3/7/07, Michael Weyrauch <michael.weyrauch at gmx.de> wrote:
>
> Dear Jean-Marc,
>
>   thanks for your fast answer.
>
> However, according to the documentation *Assumptions*
> is only an option for DEFINITE Integrals.

The option *Assumptions* works for indefinite integrals. Also, you
could use *Assuming*. For instance,

Integrate[Sign[x]/x^(1/3), x]

--> Integrate[Sign[x]/x^(1/3), x]

Assuming[x \[Element] Reals, Integrate[Sign[x]/x^(1/3), x]]

--> Piecewise[{{-((3*x^(2/3))/2), x <= 0}}, (3*x^(2/3))/2]

Integrate[Sign[x]/x^(1/3), x, Assumptions -> x \[Element] Reals]

--> Piecewise[{{-((3*x^(2/3))/2), x <= 0}}, (3*x^(2/3))/2]

> But, I must admit, I tried to give *Assumptions*
> already before your mail without success.

About your integral, you will see below that using assumtion helps
Mathematica at least to give up the evaluation in a resonable amount
of time.

rep = {b1 -> a1 + t, b2 -> a2 + t, b3 -> a3 + t, b4 -> a4 + t};

test = -((1/((b1*b3 - t13^2)^3*((-b2)*b4 + t24^2)^2))*(b3*b4*t13^2*((-b2)*b4 +
 t24^2) - b1^2*b3*(b2*b4^2 - b4*t24^2 +  b3*(b4^2 + t24^2)) +
b1*((-b2)*b4^2*(b3^2 +
 t13^2) + b3^2*b4*t24^2 +  b4*t13^2*t24^2 +  b3*t13^2*(b4^2 +
t24^2)))) /. rep;

Timing[Assuming[{a1, a2, a3, a4, t13, t24} \[Element] Reals,
Integrate[test, t]]][[1]]

--> 75.36*Second

Timing[Integrate[test, t, Assumptions -> {a1, a2, a3, a4, t13, t24}
\[Element] Reals]][[1]]

--> 96.843*Second

HTH,
Jean-Marc

> Regards    Michael


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