unsolvable indefinite integral wolfram mathematica

Of course, it's easier to use one of these programs, or, if you're writing something bigger, use one of these as libraries. If you really want to code it yourself, you can look at the source code of Sage or the several projects listed among its components. if you look at Risch's 'algorithm' posted in other answers, or symbolic integration, you can see that there are entire multi-volume books ('Manuel Bronstein, Symbolic Integration Volume I: Springer') that have been written on the topic, and very few existing computer algebra systems implement it in maximum generality. It does not handle integrals in terms of unknown functions such as g(x) and. It is a lifetime's work for some people, e.g.

If you want to do it in the most general case possible, you'll have to do much of the work that computer algebra systems do. This is doable if you don't need much generality: it's very easy to write a program that integrates polynomials, for example. You keep a set of basic forms you know the integrals of (polynomials, elementary trigonometric functions, etc.) and you use them on the form of the input.

Unsolvable indefinite integral wolfram mathematica