Maxima Function
antidiff (expr, x, u(x))
Returns an antiderivative of expr with respect to x. The expression expr may contain an unknown function u and its derivatives.
When antidiff
succeeds entirely,
the resulting expression is free of integral signs (that is, free of the integrate
noun).
Otherwise, antidiff
returns an expression
which is partly or entirely within an integral sign.
If antidiff
cannot make any progress,
the return value is entirely within an integral sign.
load ("antid")
loads this function.
The antid
package also defines the functions nonzeroandfreeof
and linear
.
antidiff
is related to antid
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 /