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MathGroup Archive 2001

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Re: Simple indefinite integral disagrees with table

  • To: mathgroup at smc.vnet.net
  • Subject: [mg28662] Re: Simple indefinite integral disagrees with table
  • From: Adam Smith<adam.smith at hillsdale.edu>
  • Date: Sat, 5 May 2001 04:00:46 -0400 (EDT)
  • References: <9ctb6k$m4h@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Your problem is in syntax.  For functions in Mathematica like Sin, Cos, Exp,
etc. you must use a square bracket for the argument.  I eliminated the "double"
xx and aa for simplicity.

In[16]:=
Integrate[x*Cos[a*x], x]

Out[16]=
Cos[a*x]/a^2 + (x*Sin[a*x])/a

Which agrees with the integral tables.

When you type:
Integrate[x Cos (a x), x], Mathematica interprets this as having 3 variables.
One is named "a", the 2nd is "Cos" and has no relation to the Cos[] function,
the third is x.  So x Cos (a x) is "multiplied out" giving Cos*a*x^2.  The
integral of x^2 with respect to x is 1/3 x^3 and Mathematica give the result of
the "constants" a and Cos times 1/3 x^3

Just a note:  If you want to raise a trig function to a power in Mathematica DO
NOT try Cos^2[x].  In mathematica this is Cos[x]^2.  This is different from:
cos(x^2) which is entered as Cos[x^2].

Adam Smith



In article <9ctb6k$m4h at smc.vnet.net>, Mitch Berkson says...
>
>The Mathematica solution to the indefinite integral below doesn't agree with
>that found in my CRC tables.
>
>Integrate[xx Cos (aa xx), xx]
>= (1/3) aa Cos xx^3
>
>The CRC table gives: (1/aa^2) Cos (aa xx) + (xx/aa) Sin (aa xx)
>
>The Mathematica solution doesn't look right.  Thanks for any help.
>
>Mitch Berkson
>
>



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