
int - definite and indefinite integration

Calling sequence:
int(f, x)
int(f, x=a..b)

Parameters:
f, a, b   --  expressions
x         --  identifier

Summary:

int(f,x) returns the antiderivative of the expression f with respect to x, or
the unevaluated call if no antiderivative in terms of elementary functions
exists.  int(f,x=a..b) returns the definite integral of f from a to b.  If a
and b are constants a numerical evaluation of the integral is obtained by
float(int(f,x=a..b)).

For details of the algorithm see:

M. Bronstein.  A Unification of Liouvillian Extension.  AAECC Applicable
Algebra in Engineering, Communication and Computing. 1:5-24,1990.

M. Bronstein.  The Transcendental Risch Differential Equation.  Journal of
Symbolic Computation. 9:49-60,1990.

H.I. Epstein and B.F. Caviness.  A Structure Theorem for the Elementary
functions and Its Application to the Identity Problem. International Journal
of Computer and Information Science. 8:9-37,1979.

K.O. Geddes, S.R. Czapor and G. Labahn. Algorithms for Computer Algebra.
1992.

>>  int(1/x/ln(x),x);

                           ln(ln(x))

>>  int(1/(x^2-8),x);

                      1/2          1/2     1/2          1/2
                     2    ln(x + 2 2   )   2    ln(x - 2 2   )
                    - ------------------- + -------------------
                             8                  8

>>  int(int(int(1,z=0..c*(1-x/a-y/b)),y=0..b*(1-x/a)),x=0..a);

                             a b c
                             -----
                               6

>>  int(sin(cos(x)),x=0..1);

                    int(sin(cos(x)), x = 0..1)

>>  float(%);

                          0.7386429979

See_also:__diff_____________________________________________________
