Final answer:
This integral is evaluated using trigonometric substitution, resulting in an expression involving the arcsine function. It is an example of an integral calculation often encountered in college-level calculus.
Step-by-step explanation:
The integral ∫(1/(\u221a(a² - x²))) dx is a common form encountered in college-level calculus, specifically when dealing with integrals involving inverse trigonometric functions. This particular form is the inverse of the sine function, or arcsin. To solve the integral, one can use the trigonometric substitution method where x = a * sin(θ), dx = a * cos(θ) dθ, and the integral becomes ∫ dθ, which equals θ.
After substitution, the result involves the arcsin function, and the limits of integration may need to be adjusted according to the substitution implemented. Therefore, the answer involves the arcsine function, and the integral translates to arcsin(x/a) + C, where C is the constant of integration.