(%i1) factor(x^3-2*x^2 - x+2);
(%o1) (x - 2) (x - 1) (x + 1)
(%i2) expand((x+1)^7);
7 6 5 4 3 2
(%o2) x + 7 x + 21 x + 35 x + 35 x + 21 x + 7 x + 1
(%i3) ratsimp(1/x - x + 1/(x+1));
3 2
x + x - 2 x - 1
(%o3) - -----------------
2
x + x
(%i4) trigreduce((sin(x)^3));
3 sin(x) - sin(3 x)
(%o4) -------------------
4
(%i1) (x^2+3)/(x^3+1);
2
x + 3
(%o1) ------
3
x + 1
(%i2) partfrac(%,x);
4 x - 5
(%o2) --------- - --------------
3 (x + 1) 2
3 (x - x + 1)
(%i3) integrate(%,x);
2 x - 1
2 9 atan(-------)
log(x - x + 1) sqrt(3)
--------------- - ---------------
4 log(x + 1) 2 sqrt(3)
(%o3) ------------ - ---------------------------------
3 3
(%i1) y(x):=(x+1)/(x-1);
x + 1
(%o1) y(x) := -----
x - 1
(%i2) diff(y(x),x,2);
2 (x + 1) 2
(%o2) --------- - --------
3 2
(x - 1) (x - 1)
(%i3) ratsimp(%);
4
(%o3) -------------------
3 2
x - 3 x + 3 x - 1
(%i4) factor(%);
4
(%o4) --------
3
(x - 1)
(%i1) f(z):= cos(2*z) / (z^2*sin(3*z));
cos(2 z)
(%o1) f(z) := -----------
2
z sin(3 z)
(%i2) taylor(f(z),z,0,6);
3 5
1 1 91 z 3751 z 138811 z
(%o2)/T/ ---- - --- - ---- - ------- - --------- + . . .
3 6 z 360 15120 604800
3 z
(%i3) residue(f(z),z,0);
1
(%o3) - -
6
(%i1) assume(a>0);
(%o1) [a > 0]
(%i2) integrate(1/(x^2+a),x);
x
atan(-------)
sqrt(a)
(%o2) -------------
sqrt(a)
(%i3) forget(a>0); assume(a<0);
(%o3) [a > 0]
(%o4) [a < 0]
(%i5) integrate(1/(x^2+a),x);
2 x - 2 sqrt(- a)
log(-----------------)
2 x + 2 sqrt(- a)
(%o5) ----------------------
2 sqrt(- a)
(%i6) integrate(sin(a*x)/x,x,minf,inf);
(%o6) - %pi