I think the best way to use a computer in learning Calculus is as a sort of solutions manual, but better. Do a problem first by hand. Then verify correctness of your solution. This is way better than what you get by using a solutions manual!

For this course its most useful to have a program that does symbolic integration. I recommend maxima, which is a fairly simple completely free and open source program written (initially) in the 1960s at MIT. Download it for free from
It's not insanely powerful, but it'll instantly do (something with) pretty much any integral in this class, and a lot more. Plus if you know lisp you can read the source code. (You could also buy Maple or Mathematica, or use a TI-89 calculator.)

Here are some maxima examples:

(%i2) integrate(x^2 + 1 + 1/(x^2+1), x);
(%o2)                          atan(x) + -- + x

(%i3) integrate(sqrt(5/x), x);
(%o3)                          2 sqrt(5) sqrt(x)

(%i4) integrate(sin(2*x)/sin(x), x);
(%o4)                              2 sin(x)

(%i5) integrate(sin(2*x)/sin(x), x, 0, %pi);
(%o5)                                  0

(%i6) integrate(sin(2*x)/sin(x), x, 0, %pi/2);
(%o6)                                  2

William Stein 2006-03-15