Evaluate the indefinite integral of f(x) = (sin x + cos x)/(sin x - cos x).

We'll determine the indefinite integral by changing the
variable.

We'll note the denominator sin x - cos x =
t(x)

We'll differentiate the
denominator:

(sin x - cos x)' = [cos x - (-sin
x)]dx

(cos x + sin x)dx
= dt

We'll notice that the numerator of the function is the
result of differentiating the function.

We'll calculate the
integral:

Int f(x) = Int
dt/t

Int dt/t = ln |t| + C

But
t = sin x - cos x

Int f(x) = ln|sin x - cos
x| + C