Trigonometric Substitution

Expression	Substitution	Relevant Identity
$\sqrt{x^2+a^2}$	$x=a\tan \theta$	${\tan }^2\theta +1={\sec }^2\theta$
$\sqrt{x^2-a^2}$	$x=a\sec \theta$	${\sec }^2-1={\tan }^2\theta$
$\sqrt{a^2-x^2}$	$x=a\sin \theta$	$1-{\sin }^2\theta ={\cos }^2\theta$