derivate(integrate(f(x))) <> f(x)!



On 7/9/07, Patrick Gelin <patrick.gelin at free.fr> wrote:
>
> f(x)=sin(x)^2*cos(x)^2
> F(x)=integrate(f(x),x)=-1/3*cos(x)^3+2/5*cos(x)^5-1/7*cos(x)^7+C
> and derivate(F(x),x) = cos(x)^6*sin(x) what is different from f(x)!


Are you sure you are using Maxima?  Maxima does not have a routine
"derivate", and the syntax you are using (F(x)=...) won't work in Maxima.
What's more, this is not the result that Maxima gives for integrate/diff in
this case:

 (%i1) f: sin(x)^2*cos(x)^2;
(%o1) cos(x)^2*sin(x)^2
(%i2) fi: integrate(f,x);
(%o2) (2*x-sin(4*x)/2)/16
(%i3) fid: diff(fi,x);
(%o3) (2-2*cos(4*x))/16

fid looks different from f, but in fact it is a different formula for the
same function.  We can use "trigrat" to get a standardized form:

(%i4) trigrat(f);
(%o4) -(cos(4*x)-1)/8

(%i5) trigrat(fid);
(%o5) -(cos(4*x)-1)/8

By the way, is it possible to look the differentes step of the calcul ?


No, sorry.

               -s