I just noticed that the following quiz problem I gave my students came
back nicer from Sage (i.e., maxima) and sympy than mathematica. Kudos
to you guys for having a better answer:
Mathematica 7.0 for Linux x86 (32-bit)
Copyright 1988-2008 Wolfram Research, Inc.
In[1]:= Integrate[Sin[x]^2*Cos[x]^5, x]
5 Sin[x] Sin[3 x] 3 Sin[5 x] Sin[7 x]
Out[1]= -------- - -------- - ---------- - --------
64 192 320 448
versus
sage: integrate(sin(x)^2*cos(x)^5,x)
1/7*sin(x)^7 - 2/5*sin(x)^5 + 1/3*sin(x)^3
sage: import sympy
sage: sympy.integrate(sin(x)^2*cos(x)^5,x)
sin(x)**3/3 - 2*sin(x)**5/5 + sin(x)**7/7
The problem is a simple integration by parts problem, and the students'
by-hand answers match the simpler answer given by maxima and sympy.
Thanks,
Jason
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