/*************** -*- Mode: MACSYMA; Package: MAXIMA -*-  ******************/
/***************************************************************************
***                                                                    *****
***     Copyright (c) 1984 by William Schelter,University of Texas     *****
***     All rights reserved                                            *****
***************************************************************************/


KILL(ALL);
DONE$
PARTITION(2*A*X*F(X),X);
[2*A,X*F(X)]$
PARTITION(A+B,X);
[B+A,0]$
2*(A*LOG(X)+2*A*LOG(Y));
2*(2*A*LOG(Y)+A*LOG(X))$
LOGCONTRACT(%);
A*LOG(X^2*Y^4)$
LOGCONTRACT(LOG(SQRT(X+1)+SQRT(X))+LOG(SQRT(X+1)-SQRT(X)));
0$
ROOTSCONMODE:FALSE;
FALSE$
ROOTSCONTRACT(X^(1/2)*Y^(3/2));
SQRT(X*Y^3)$
ROOTSCONTRACT(X^(1/2)*Y^(1/4));
SQRT(X)*Y^(1/4)$
ROOTSCONMODE:TRUE;
TRUE$
ROOTSCONTRACT(X^(1/2)*Y^(1/4));
SQRT(X*SQRT(Y))$
ROOTSCONTRACT(X^(1/2)*Y^(1/3));
SQRT(X)*Y^(1/3)$
ROOTSCONMODE:ALL;
ALL$
ROOTSCONTRACT(X^(1/2)*Y^(1/4));
(X^2*Y)^(1/4)$
ROOTSCONTRACT(X^(1/2)*Y^(1/3));
(X^3*Y^2)^(1/6)$
ROOTSCONMODE:FALSE;
FALSE$
ROOTSCONTRACT(SQRT(SQRT(X+1)+SQRT(X))*SQRT(SQRT(X+1)-SQRT(X)));
1$
ROOTSCONMODE:TRUE;
TRUE$
ROOTSCONTRACT(SQRT(SQRT(5)+5)-5^(1/4)*SQRT(SQRT(5)+1));
0$
KILL(F,G,H,X,Y);
DONE$
DIFF(SIN(X)+X^3+2*X^2,X);
COS(X)+3*X^2+4*X$
DIFF(SIN(X)*COS(X),X);
COS(X)^2-SIN(X)^2$
DIFF(SIN(X)*COS(X),X,2);
-4*COS(X)*SIN(X)$
DERIVABBREV:TRUE;
TRUE$
DIFF(EXP(F(X)),X,2);
%E^F(X)*'DIFF(F(X),X,2)+%E^F(X)*('DIFF(F(X),X,1))^2$
'INTEGRATE(F(X,Y),Y,G(X),H(X));
'INTEGRATE(F(X,Y),Y,G(X),H(X))$
DIFF(%,X);
'INTEGRATE('DIFF(F(X,Y),X,1),Y,G(X),H(X))
 +F(X,H(X))*'DIFF(H(X),X,1)-F(X,G(X))*'DIFF(G(X),X,1)$
KILL(A,X,F,Y,T);
DONE$
DEPENDS(A,X);
[A(X)]$
DIFF(A . A,X);
'DIFF(A,X,1) . A+A . 'DIFF(A,X,1)$
DEPENDS(F,[X,Y],[X,Y],T);
[F(X,Y),X(T),Y(T)]$
DIFF(F,T);
'DIFF(F,Y,1)*'DIFF(Y,T,1)+'DIFF(F,X,1)*'DIFF(X,T,1)$
DEPENDS(Y,X);
[Y(X)]$
KILL(F,G,J);
DONE$
GRADEF(F(X,Y),X^2,G(X,Y));
F(X,Y)$
DIFF(F(X,Y),X);
G(X,Y)*'DIFF(Y,X,1)+X^2$
GRADEF(J(N,Z),'DIFF(J(N,Z),N),J(N-1,Z)-N/Z*J(N,Z));
J(N,Z)$
RATSIMP(DIFF(J(2,X),X,2));
(J(0,X)*X^2-3*J(1,X)*X+6*J(2,X))/X^2$
TEST(F):=BLOCK([U],U:INTEGRATE(F,X),RATSIMP(F-DIFF(U,X)));
TEST(F):=BLOCK([U],U:INTEGRATE(F,X),RATSIMP(F-DIFF(U,X)))$
TEST(SIN(X));
0$
TEST(1/(1+X));
0$
TEST(1/(1+X^2));
0$
INTEGRATE(SIN(X)^3,X);
COS(X)^3/3-COS(X)$
KILL(Q);
DONE$
INTEGRATE(%E^X/(%E^X+2),X);
LOG(%E^X+2)$
INTEGRATE(1/(X*LOG(X)),X);
LOG(LOG(X))$
INTEGRATE(SIN(2*X+3),X);
-COS(2*X+3)/2$
INTEGRATE(%E^X*ERF(X),X);
%E^X*ERF(X)-%E^(1/4)*ERF(X-1/2)$
INTEGRATE(X/(X^3+1),X);
LOG(X^2-X+1)/6+ATAN((2*X-1)/SQRT(3))/SQRT(3)-LOG(X+1)/3$
DIFF(%,X);
2/(3*((2*X-1)^2/3+1))+(2*X-1)/(6*(X^2-X+1))-1/(3*(X+1))$
RATSIMP(%);
X/(X^3+1)$