Is there a javascript library that can find complex integrals and take the inverse function?

Question

JavaScript

I need a library (in js) that can recognize mathematical expressions written in a string (supports symbolic arithmetic) and that can do 2 operations:
1) find (complex) antiderivative functions
like: 3*sin(2*x)*cos(x)^4or 3*sin(2*x)*sin(x)^4
2) find (complex) inverse functions
like: -acos(x)^6or sin(x)^6
I have tried libraries like algebrite , nerdamer , mathjs
but they are not capable of that.
Is there a js library that can do this? Maybe a js port of some library that was written in another language? It is desirable that the library be as capable (in terms of these 2 operations) as wolframalpha or at least asMaxima system

Answer 1

Actually, your queries require a huge database. And even with it, most problems do not have a solution: sin(x/xit is not integrated and does not have an inverse function - more precisely, everything is possible, but it is not expressed in elementary functions.

Answer 2

Even a trained student and professor will not always take some tricky integral, even if it is taken in elementary functions. You have a task of the level "you need a library that, according to the description of the task, returns an algorithm for solving it." In short, there is no such thing. wolframalpha has a large set of table integrals and tries a bunch of different methods, but it doesn't work on all integrals.

Answer 3

Use web api from wolframalpha: https://products.wolframalpha.com/api/
There are also js libraries
API sandbox https://products.wolframalpha.com/api/explorer/