Nice Integrate setting

• To: mathgroup at smc.vnet.net
• Subject: [mg73104] Nice Integrate setting
• From: "dimitris" <dimmechan at yahoo.com>
• Date: Fri, 2 Feb 2007 05:43:48 -0500 (EST)

```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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