u = 1+3e-x
so that (Don't forget to use the chain rule on e-x.)
du = 3e-x(-1) dx = -3e-x dx ,
or
(-1/3)du = e-x dx .
However, how can we replace the term e-3x in the original problem ? Note that
.
From the u-substitution
u = 1+3e-x ,
we can "back substitute" with
e-x = (1/3)(u-1) .
Substitute into the original problem, replacing all forms of x, getting
(Recall that (AB)C = AC BC .)
