Integrals of Form ∫ dx/(a sin x + b cos x)

Express denominator as $$ R \sin(x \pm \alpha) $$ or $$ R \cos(x \mp \alpha) $$ where
$$ R = \sqrt{a^2 + b^2} $$
Then $$ \int \frac{dx}{a \sin x + b \cos x} = \frac{1}{\sqrt{a^2+b^2}} \ln \left| \tan \frac{x \pm \alpha}{2} \right| + C $$