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/*************** -*- 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$
expand(rootscontract(x^(1/2)*y^(1/4)) - sqrt(x*sqrt(y)),0,0);
0$
expand(rootscontract(x^(1/2)*y^(1/3)) - sqrt(x)*y^(1/3),0,0);
0$
rootsconmode:all;
all$
expand(rootscontract(x^(1/2)*y^(1/4)) - (x^2*y)^(1/4),0,0);
0$
expand(rootscontract(x^(1/2)*y^(1/3)) -(x^3*y^2)^(1/6),0,0);
0$
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$
/* Correct simplification after change to risch.lisp revision 1.17 */
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)$
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