The domain of integration for the function 1/(1-x^2y^2) is the set of all real numbers except for x values that make the denominator equal to zero, which in this case are x = ±1/y.
Yes, the function 1/(1-x^2y^2) is integrable as it is continuous and defined on a finite interval.
The integral of 1/(1-x^2y^2) dx can be solved using the substitution method, where u = xy and du = ydx. The integral then becomes ∫1/(1-u^2) du, which can be solved using partial fraction decomposition.
Yes, the integral of 1/(1-x^2y^2) dx can also be solved using trigonometric substitutions or by converting it into a rational function using the substitution x = tanθ.
The function 1/(1-x^2y^2) is important in mathematics as it is a common type of integral that appears in many applications, such as in physics and engineering. It is also used in solving differential equations and in the study of series and sequences.