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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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