I see no easy way to do this because you must divide a product
up into u' and v in some magical way.
If you write a program that does that,
say,
marcmagic(expression) := computes something and returns a list,
[uprime, v]
then the rest is easy.
intbypart(expression,x,a,b):=
block([ z:marcmagic(expression),u],
u: integrate(part(z,1), x,a,b),
u*part(z,2) - integrate(u* diff(part(z,2),x,a,b));
dividing a product into pieces when there are not exactly two pieces
is not only a combinatorial process, but requires some cleverness.
e.g. sin(2*x) is a product, namely 2* cos(x) * sin(x).
Maxima tries integration by parts as one of the methods in
its indefinite integration program, but actually uses it much
less than humans do.
RJF
Marc Hodapp wrote:
> 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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