prolog rules for integral calculus symbolic computation

gistfile1.prolog

   /****************** Integral Calculus ***************/
int( 0 , X , 0).
 
int( C , X , C * X ):-
        atomic(C),
        C \= X,  !.
 
int( X , X , 0.5 * X^2 ):- !.
 
int( 1 / X , X , ln(X) ):- !.
 
int( C * X , X , C * R):-
        atomic(C),
        int(X , X , R).
 
int( X * C , X , R):-
        atomic(C),
        int(C * X , X , R).
 
int( U + V , X , A + B ):-
        int( U , X , A ),
        int( V , X , B ).
 
int( U - V , X , A - B):-
        int( U , X , A ),
        int( V , X , B ).
 
int( U * V , X , U * R):-
        atomic(U),
        U \= X,
        int(V , X , R).
 
int( A^X , X , A^X / ln(A) ):-
        atomic(A),
        A \= X,
        !.
 
int( X^N , X , W1 * (X ^ W ) ):-
        numeric(N),
        W is N + 1,
        W1 is 1 / W,
        !.
 
int( X^N , X , (1 / (N + 1) ) * X ^ (N + 1) ):-
        atomic(N),
        !.
 
int( Z / X , X , Z * ln(X) ):-
        atomic(Z),
        Z \= X, !.
 
int( ( (A*X+B)^(-1) ) * X , X , inf ).
 
int( ( (A*X+B)^N ) * X , X , R):-
        A1 = ( A*X + B) ^ ( N + 1),
        A2 = ( A * ( N + 1 ) ),
        R = A1 / A2.
 
int( sin(A*X+B) , X , -(1/A) * cos(A*X+B) ):- !.
 
int( cos(A*X+B) , X , (1/A) * sin(A*X+B) ):- !.
 
% integration of functions
int( sin(X) , X , -cos(X) ):- !.
 
int( cos(X) , X , sin(X) ):- !.
 
int( tan(X) , X , ln(cos(X)) ):- !.
 
int( sec(X) , X , ln( sec(X) + tan(X) ) ):- !.
 
int( cosec(X) , X , ln( cosec(X) - cot(X) ) ):-        !.
 
int( cot(X) , X , ln(sin(X)) ):- !.
 
int( exp(X) , X , exp(X) ):- !.
 
int( sec(X)^2 , X , tan(X) ):- !.
 
int( cosec(X)^2 , X , -cot(X) ):- !.
 
int( sec(X) * tan(X) , X , sec(X) ):- !.
 
int( cosec(X) * cot(X) , X , -cosec(X) ):- !.
 
int( 1/(A*X+B) , X , (1/A) * ln(A*X+B) ):- !.
 
int( exp(A*X+B) , X , (1/A) * exp(A*X+B) ):- !.
 
int( 1/sqrt(1-X^2) , X , arcsin(X) ):- !.
 
int( 1/sqrt(1+X^2) , X , arctan(X) ):- !.
 
int( 1/(X*sqrt(X^2-1)) , X , arcsec(X) ):- !.
 
int( 1/(X^2-A^2) , X , (1/2*A) * ln( (X-A) / (X+A) ) ):- !.
 
int( 1/(A^2-X^2) , X , (1/2*A) * ln( (A+X) / (A-X) ) ):- !.
 
int( 1/(X^2+A^2) , X , (1/A)* arctan(X/A) ):- !.
 
int( 1/sqrt(X^2-A^2) , X , ln( X+sqrt(X^2-A^2) ) ):- !.
 
int( 1/sqrt(A^2-X^2) , X , arcsin(X/A) ):- !.
 
int( 1/sqrt(A^2+X^2) , X , ln(X+sqrt(X^2+A^2)) ):- !.
 
% integration of functions
% using substitutions
 
int( sin(X)*cos(X), X , (1/2)*R):-
        int(sin(2*X),X,R).
 
%if all fails
 
int(W,X,W).
   /****************** End Integral Calculus ***************/