[/URL]Pseudo Statistic said:This is what http://integrals.wolfram.com gave me:
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An elementary solution in mathematics refers to an analytical expression or function that can be expressed using basic mathematical operations, such as addition, subtraction, multiplication, division, and exponentiation. It also includes commonly used mathematical functions, such as polynomials, trigonometric functions, and exponential functions.
An integral in mathematics is a mathematical concept that represents the area under a curve on a graph. It is used to find the total value of a continuous variable over a given interval. Integrals are commonly used in calculus and are essential in solving many real-world problems in physics, engineering, and economics.
An integral can be difficult to solve when it does not have an elementary solution. This means that the integral cannot be expressed using basic mathematical functions and operations. In such cases, more advanced techniques, such as numerical integration or approximations, may be used to find an approximate solution.
There is no general method for determining if an integral has an elementary solution. However, there are some techniques, such as the Risch algorithm, that can be used to determine if a given integral has an elementary solution. In some cases, it may also be possible to prove that an integral does not have an elementary solution.
Some examples of integrals that have elementary solutions include polynomial integrals, trigonometric integrals, exponential integrals, and logarithmic integrals. These types of integrals can be solved using basic integration techniques, such as substitution, integration by parts, or partial fractions.