Maxima Function
antid (expr, x, u(x))
Returns a two-element list, such that an antiderivative of expr with respect to x can be constructed from the list. The expression expr may contain an unknown function u and its derivatives.
Let L, a list of two elements, be the return value of antid
.
Then L[1] + 'integrate (L[2], x)
is an antiderivative of expr with respect to x.
When antid
succeeds entirely,
the second element of the return value is zero.
Otherwise, the second element is nonzero,
and the first element is nonzero or zero.
If antid
cannot make any progress,
the first element is zero and the second nonzero.
load ("antid")
loads this function.
The antid
package also defines the functions nonzeroandfreeof
and linear
.
antid
is related to antidiff
as follows.
Let L, a list of two elements, be the return value of antid
.
Then the return value of antidiff
is equal to L[1] + 'integrate (L[2], x)
where x is the variable of integration.
Examples:
(%i1) load ("antid")$ (%i2) expr: exp (z(x)) * diff (z(x), x) * y(x); z(x) d (%o2) y(x) %e (-- (z(x))) dx (%i3) a1: antid (expr, x, z(x)); z(x) z(x) d (%o3) [y(x) %e , - %e (-- (y(x)))] dx (%i4) a2: antidiff (expr, x, z(x)); / z(x) [ z(x) d (%o4) y(x) %e - I %e (-- (y(x))) dx ] dx / (%i5) a2 - (first (a1) + 'integrate (second (a1), x)); (%o5) 0 (%i6) antid (expr, x, y(x)); z(x) d (%o6) [0, y(x) %e (-- (z(x)))] dx (%i7) antidiff (expr, x, y(x)); / [ z(x) d (%o7) I y(x) %e (-- (z(x))) dx ] dx /