∫ d u a 2 − u 2 = arcsin ( u a ) + C {\displaystyle \int {\frac {du}{\sqrt {a^{2}-u^{2}}}}=\arcsin \left({\frac {u}{a}}\right)+C}
∫ d u a 2 + u 2 = 1 a arctan ( u a ) + C {\displaystyle \int {\frac {du}{a^{2}+u^{2}}}={\dfrac {1}{a}}\arctan \left({\dfrac {u}{a}}\right)+C}
∫ d u u u 2 − a 2 = 1 a arcsec ( | u | a ) + C {\displaystyle \int {\frac {du}{u{\sqrt {u^{2}-a^{2}}}}}={\frac {1}{a}}\operatorname {arcsec} \left({\dfrac {|u|}{a}}\right)+C}
Integration into Inverse trigonometric functions using Substitution by The Organic Chemistry Tutor
Integrating using Inverse Trigonometric Functions by patrickJMT
