1)
(b)
> t^2*BesselJ(3,t): eq2 := "=expand(");
> rhs(eq2)-4*rhs(eq1) = lhs(eq2)-4*lhs(eq1);
> normal((rhs(")-lhs("))/t=0
);
> expand(");
(b)
>
simplify(f);
(c)
>
simplify(f,symbolic);
(b)
>
(x^5+40*x^4+595*x^3+3905*x^2+9680*x+1331)^(1/3);
>
simplify(");
>
simplify(",symbolic);
>
(x^3)^(1/3);
>
simplify(",assume=positive);
>
simplify("",assume=negative);
(c)
>
(x-2)^(3/2)/(x^2-4*x+4)^(1/4);
>
simplify(");
>
simplify(",symbolic);
(d)
>
(sqrt(x)-y)/(x-y^2);
>
subs(x=s^2,");
>
simplify(",assume=positive);
>
subs(s=sqrt(x),");
(e)
>
1/(2+5^(1/3));
>
rationalize(");
(f)
>
cos(x+y)+sin(x)*sin(y)+2^(x+y);
>
expand(",2^(x+y));
(g)
>
2*cos(x)^2-cos(2*x);
>
simplify(");
(b)
>
int( 1/(x^4-4), x );
>
diff(",x);
>
normal("",expanded);
(c)
>
int( sin(3*x)*cos(2*x), x );
>
diff(",x);
>
subs(5*x=y,2*");
>
readlib(trigsubs)(");
>
subs( y=5*x, op(")/2 );
>
";
>
int( sin(3*x)*cos(2*x), x );
>
diff(",x);
>
expand( " - sin(3*x)*cos(2*x) );
(b)
>
ln( tan(1/2*x+Pi/4)) -
>
arcsinh( tan(x) ) = 0;
>
testeq(");
>
f := lhs("");
>
diff(f,x);
>
expand(");
>
simplify(",symbolic);
>
subs(x=0,f);
>
evalf(");
(c)
>
tan(x)+tan(y) = sin(x+y)/(cos(x)*cos(y));
>
testeq(");
>
simplify( lhs("") - expand(rhs("")) );
(d)
>
sin(5*x) = 5*sin(x) -20*sin(x)^3 +
>
16*sin(x)^5;
>
testeq(");
>
expand( lhs("") );
>
simplify(", {cos(x)^2+sin(x)^2=1},
>
[cos(x),sin(x)] );