Partial integration with maxima



What do you think of :

 (C1) intpart(u,v,a,b):=subst(x=b,integrate(u,x))*subst(x=b,v)-
subst(x=a,integrate(u,x))*subst(x=a,v)-integrate(integrate(u,x)*diff(v,x),x,a,b);

(D1) intpart(u,v,a,b):=SUBSTITUTE(x=b,INTEGRATE(u,x)) SUBSTITUTE(x=b,v) - 
SUBSTITUTE(x=a,INTEGRATE(u,x)) SUBSTITUTE(x=a,v) - INTEGRATE(INTEGRATE(u,x) 
DIFF(v,x),x,a,b)

Examples :

(C2) 'integrate(x*log(x),x,1,%e)=intpart(x,log(x),1,%e);

(C4) 'integrate(x*exp(2*x),x,0,1)=intpart(x,exp(2*x),0,1);

(D5) 'integrate(x^n*sin(x),x,0,%pi/2)=intpart(x^n,sin(x),0,%pi/2);

Maxima will not do the job alone...

Le mercredi 14 Septembre 2005 13:32, Marc Hodapp a écrit :
> Hi everybody,
>
> how can I perform an integration by parts like
>
>  b                               b
>  /                      b        /
>
>  | u'*v dx = [u*v]      -  |  u*v' dx
>
> /                       a       /
> a                              a
>
> with maxima?  u and v are functions of x by the way.
>
> Many thanks in advance.
>
> Marc Hodapp
>
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