Evaluate the integral ∫ (cos(x^2)) dx.

The integral of ( \cos(x^2) ) does not have a simple closed form, which means that it cannot be expressed in terms of elementary functions (like polynomials, exponentials, logarithms, trigonometric functions, etc.). Instead, the evaluation of this integral is typically done using special functions or numerical methods.

For functions like ( \cos(x^2) ), mathematicians often resort to techniques involving Fresnel integrals or series expansions. These functions do not possess a neat algebraic or trigonometric expression that would allow for an easy representation of the integral.

In the context of standard calculus practice, it’s important to recognize new and complex patterns that transcend basic techniques, as revealing the limits of integration emphasizes the significance of exploring special functions in advanced mathematical contexts.

Therefore, stating that the integral may be tempting to suggest has a simple form may lead to confusion, as it leads one to overlook the rich structure of mathematics that encompasses functions beyond the elementary category. The conclusion reached aligns with established mathematical knowledge that recognizes the limitations of elementary function integration when dealing with integrals of forms like ( \cos(x^2) ).