- You can try similar problems (not in the homework) and also verify your answers. This is like playing solitaire, but is much more creative.
- You can verify key steps of what you did by hand using the
computer. E.g., if you're confused about one of part of
*your*approach to computing an integral, you can compare what you get with the computer. Solution manuals either give you only the solution or a particular sequence of steps to get there, which might have little to do with the brilliantly original strategy you invented.

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

Here are some maxima examples:

(%i2) integrate(x^2 + 1 + 1/(x^2+1), x); 3 x (%o2) atan(x) + -- + x 3 (%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