When the integrand includes certain expressions that includes variables and constant values that are perfect squares, a set of trigonmetric substitutions can be used. This page describes specific substitions when encountering integrands of any of the following forms:
$\sqrt{{a}^{2}-{x}^{2}}\sqrt{{a}^{2}+{x}^{2}}\sqrt{{x}^{2}-{x}^{2}}$