Manipulating Integrals
I’ve written previously about Mathematica. I’m going to describe a really cool feature that none of the other symbolic manipulation programs have.
Integrating

depends on the value of n. If n equals 1, then the integral value
is Log(x). Otherwise it’s just x^(-n+1)/(-n+1). Mathematica allows
one to manipulate the value of n in realtime. Here are three screenshots
with n={0,1,2}.

I wish I had this when I was studying Calculus for the first time!