       Re: Nice Integrate setting

• To: mathgroup at smc.vnet.net
• Subject: [mg73187] Re: Nice Integrate setting
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Tue, 6 Feb 2007 04:11:15 -0500 (EST)
• Organization: Uni Leipzig
• References: <epv37b\$8ej\$1@smc.vnet.net>

```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:
>
>
> IIn:=
> Integrate[Log[x], x]
> Integrate[%, x]
> Integrate[%, x]
> Simplify[%]
>
> Out=
> -x + x*Log[x]
>
> Out=
> -((3*x^2)/4) + (1/2)*x^2*Log[x]
>
> Out=
> -((11*x^3)/36) + (1/6)*x^3*Log[x]
>
> Out=
> (1/36)*x^3*(-11 + 6*Log[x])
>
> one can simply execute the command
>
> In:=
> Integrate[Log[x], x, x, x]
>
> Out=
> (1/36)*x^3*(-11 + 6*Log[x])
>
> Similarly,
>
> In:=
> Timing[Integrate[Cos[x^2], x, x, x, x, x, x]]
>
> Out=
> {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:=
> (TableForm[#1, TableAlignments -> Center] & )[({#1, Integrate[1/
> Sqrt[x], Sequence @@ Table[x, {#1}]]} & ) /@ Range]
>
> BTW, the D function can also take the same setting
>
> In:=
> D[BesselJ[0, x], {x, 5}] == D[BesselJ[0, x], x, x, x, x, x]
>
> Out=
> True
>
> Dimitris
>

```

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