integrals can be expressed by elementary functions, and that means that theoretically, as long as we areable to effectuate related algebraic computations (like computations of roots of the denominator), wewill also be able to find an exact formula for the integral. Moreover, many other types of integrals canbe reduced, by special substitutions, to integrals of rational functions. However, this is not the case forall elementary functions. There are many known functions with integrals that can not be expressed byelementary functions, i.e. it is impossible to express them by an analytic formula using basic elementaryfunctions, arithmetic operations, their compositions and inverses. The following are just few well knownintegrals that can not be expressed by elementary functions:∫e−x2dx, ,∫sinx2dx,∫cos2xdx∫sinxxdx,∫cosxxdx,∫dxlnx,but there are many more.