I'm new to using Wolfram Alpha for teaching, having switched from Maple.
When teaching calculus with Maple in our computer lab, I had students use the "changevar" command as a tool for gaining an intuition of what makes an appropriate substitution when discussing the integration by substitute method. For example,
Original:=Int((cos(x)+1)^3*sin(x),x)
New:=changevar(cos(x)+1=U,Original,U)
takes the original integral and constructs a new integral in terms of the variable, U. The idea is to get students to experiment with various choices for U, see what works best, and perform the algebra/substitution details outside of class.
There is an analogous tool for integration by parts.
Are there similar commands in Wolfram Alpha?