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 > >