




Suppose our integrand is a rational function of sin(x) and cos(x).
After the substitution z = tan(x / 2) we obtain an integrand that is a rational function of z, which can then be evaluated by partial fractions.
Theorem:
If z = tan(x / 2), then
,
,
and
and any rational function of xdx becomes a rational function of zdz.
_{Proof}
_{Example}