changevar problem with sin(x)+cos(x)=t



Dear members of maxima list

Maxima cannot change variables in the following integral

changevar('integrate(
(sin(x)+cos(x))/sqrt(sin(x)-cos(x)),x
),sin(x)-cos(x)=t,t,x);

the problem is probably caused by the fact that maxima cannot solve
sin(x)+cos(x)=t with respect to t

Is there any workaround for this? Is there any way how to transform the
integral of f'(x)g(f(x)) into g(t)  ?
here f' denotes derivative.

I suppose that it is difficult to write a function which solves similar
problem in general, but maybe someone worked in this direction.

Thank you

Robert Marik