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
the output was
1- What exactly is r1 ??
A way out (see this thread) seems to make of the solution a function of
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?