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How to find indefinite integral for a function whose original function is not an elementary function?
Since the landlord mentioned the concept of forced retention, he is obviously no longer Xiao Bai. However, have you ever considered what an elementary function is?

In fact, there is another concept related to elementary functions, and that is simple functions. These two concepts can be found in more basic and abstract mathematical fields, such as measure theory. ), we won't expand here-the landlord is not Xiaobai.

Back to the problem itself. At the level of definite integral, there are so-called normal distribution table and gamma function, which are not elementary functions, but definite integral. The upper and lower bounds of the gamma function are still fixed, and the reason why it is a definite integral is mainly because it is really difficult to give an analytical solution to its indefinite integral, thus giving a numerical solution (there is also a more realistic reason that those solutions are used in some places, that is, the numerical solution is very practical). The reason why it can't be done is that people who dare to generate can provide a universal way, as long as they are embedded in the formula, there is no exception, and such integrals are really varied, and there are even integrand functions without analytical expressions, so it is naturally unrealistic to solve them once and for all.

In addition, there are two propositions in mathematics: existence proof and solution. The former only proves that there is a solution but cannot give a specific solution, such as the integral mean value theorem; Solution is a method to give a concrete solution, and sometimes the method to prove the existence of the solution is direct solution. For example, the method to prove the existence of a matrix similar to Jordan canonical form is realized by direct solution, which is obviously convincing but more difficult to obtain.

For this reason, once a general solution can be obtained, even if it is only for a specific situation, it is enough for a paper. Therefore, instead of struggling here, it is better to find a way to solve it yourself. Good luck to you.