Following the change of variable thread, I wanted to streamline the whole process.
Namely, using the same example in the above thread, I'd like to say
integral_def_change(x*cos(x^2+1), (x, 0, 2*pi), u==x^2+1, u)
The difference is, I wanted also Sage to automatically solve for x instead of providing x= sqrt(u-1), say. But when I tried
solve(u==x^2+1, x)[0].rhs()
the output was r1
???
1- What exactly is r1 ??
A way out (see this thread) seems to make of the solution a function of u
f(u)=solve(u==x^2+1, x)[0].rhs()
Now f is
u |--> -sqrt(u - 1)
2- What can I do to get +sqrt(u - 1) instead? Is this related to the positive function question there?