antid SciMax Toolbox antisymmetric

SciMax Toolbox >> antidiff

antidiff

Maxima Function

Calling Sequence

antidiff (expr, x, u(x))

Description

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
                  /
antid SciMax Toolbox antisymmetric