Let #f(x)# be a rational function of #x# and #sqrt(x^2-a^2)#: #int f(x)dx = int R(atant, asect)sec^2t dt#ī. Substitute: #x = atant#, #dx = asec^2tdt# with #t in (-pi/2,pi/2)# and use the trigonometric identity:Ĭonsidering that for #t in (-pi/2,pi/2)# the secant is positive: Let #f(x)# be a rational function of #x# and #sqrt(x^2+a^2)#: In general trigonometric substitutions are useful to solve the integrals of algebraic functions containing radicals in the form #sqrt(x^2+-a^2)# or #sqrt(a^2+-x^2)#.
