### Symbolic solve

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 == x^2 + 1, u)

The difference is, I wanted also Sage to automatically solve for `x`

instead of providing

`x `~~instead of providing x= sqrt(u-1), ~~= sqrt(u - 1)

, say. But when I tried

~~solve(u==x^2+1, ~~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, ~~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) ~~1)

instead? Is this related to ~~the ~~the
positive function question there?