Take
, so that
and
. Note that this assumes
and so requires
.
Now take
, so that
. Note that for this invertibility condition to hold, we require that
, which means
. But since we already fixed
with the previous substitution, we thus have
, which in turn restricts us to
. So with this substitution, we have
, which gives
Now over the interval
, we have
, which means
, and so the integral is equivalent to