Re: Nice Integrate setting

• To: mathgroup at smc.vnet.net
• Subject: [mg73238] Re: Nice Integrate setting
• From: "dimitris" <dimmechan at yahoo.com>
• Date: Thu, 8 Feb 2007 03:42:55 -0500 (EST)
• References: <epv37b\$8ej\$1@smc.vnet.net><eq9cgh\$nar\$1@smc.vnet.net>

```Hello, Jens-Peer.

Indeed, I was surprized.
I didn't think the indefinite integration

Integrate[f[x],x,x,x]

as a "special case" of

Integrate[f[x,y,z],x,y,z]

So who needs the documentation?
Not me, haha!

Best Regards
Dimitris

=CF/=C7 Jens-Peer Kuska =DD=E3=F1=E1=F8=E5:
> Hi,
>
> and it become more surprising ! you can also
> Integrate[f[x,y,z],z,y,x]
>
> that's called multiple integration.
>
> Regards
>    Jens
>
> dimitris wrote:
> > I noticed a nice undocumentated (possibly ???) setting of Integrate
> > which I am sure
> > it is known to the Mathematica gurus of this forum but I think it
> > deserves to be
> > mentioned:
> >
> > Instead of something like
> >
> > IIn[12]:=
> > Integrate[Log[x], x]
> > Integrate[%, x]
> > Integrate[%, x]
> > Simplify[%]
> >
> > Out[12]=
> > -x + x*Log[x]
> >
> > Out[13]=
> > -((3*x^2)/4) + (1/2)*x^2*Log[x]
> >
> > Out[14]=
> > -((11*x^3)/36) + (1/6)*x^3*Log[x]
> >
> > Out[15]=
> > (1/36)*x^3*(-11 + 6*Log[x])
> >
> > one can simply execute the command
> >
> > In[16]:=
> > Integrate[Log[x], x, x, x]
> >
> > Out[16]=
> > (1/36)*x^3*(-11 + 6*Log[x])
> >
> > Similarly,
> >
> > In[20]:=
> > Timing[Integrate[Cos[x^2], x, x, x, x, x, x]]
> >
> > Out[20]=
> > {0.6399999999999988*Second, (1/960)*(Sqrt[2*Pi]*x*(-15 +
> > 4*x^4)*FresnelC[Sqrt[2/Pi]*x] -
> >     2*(9*x^2*Cos[x^2] + 10*Sqrt[2*Pi]*x^3*FresnelS[Sqrt[2/Pi]*x] +
> > 2*(-2 + x^4)*Sin[x^2]))}
> >
> > and so on
> >
> > e.g.
> >
> > In[23]:=
> > (TableForm[#1, TableAlignments -> Center] & )[({#1, Integrate[1/
> > Sqrt[x], Sequence @@ Table[x, {#1}]]} & ) /@ Range[10]]
> >
> > BTW, the D function can also take the same setting
> >
> > In[25]:=
> > D[BesselJ[0, x], {x, 5}] == D[BesselJ[0, x], x, x, x, x, x]
> >
> > Out[25]=
> > True
> >
> > Dimitris
> >

```

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