Table

Integrand Contains	Substitution	Based on the Identity
$\sqrt{a^{2}-x^{2}}$	$x=a\sin \theta$ , $-\dfrac{\pi }{2} \le \theta \, \le \dfrac{\pi }{2}$	$1-\sin ^{2}\theta =\cos ^{2}\theta$
$\sqrt{x^{2}+a^{2}}$	$x=a\tan \theta$ , $-\dfrac{\pi }{2} \lt\theta \lt\dfrac{\pi }{2}$	$\tan ^{2}\theta +1=\sec ^{2}\theta$
$\sqrt{x^{2}-a^{2}}$	$x=a\sec \theta$ , $0 \le \theta \lt\dfrac{\pi }{2}$ , $\pi \le \theta \lt\dfrac{3\pi }{2}$	$\sec ^{2}\theta -1=\tan ^{2}\theta$

Table 2: Table 2