Trigonometric functions of inverse trigonometric functions are tabulated below. For the special antiderivatives involving trigonometric functions, see Trigonometric integral. This substitution can sometimes simplify integrals involving trigonometric functions. The inverse trigonometric functions are partial inverse functions for the trigonometric functions. In mathematics, the trigonometric integrals are a family of integrals involving trigonometric functions. Tables of logarithms and trigonometric functions were common in math and science textbooks. Mathematical and navigation handbooks included tables of the logarithms of trigonometric functions as well. Algebraic skills are exercised with trigonometric functions and trigonometric identities. The following table summarizes the simplest algebraic values of trigonometric functions. The following is a list of integrals (antiderivative functions) of trigonometric functions. Automorphic functions then generalize both trigonometric and elliptic functions. These considerations are particularly important for defining the inverses of trigonometric functions. Another proof is based on differential equations satisfied by exponential and trigonometric functions. This is the content of the Weierstrass theorem on the uniform density of trigonometric polynomials. There are several notations used for the inverse trigonometric functions.