I think the really neat piece of software behind this is maxima (https://maxima.sourceforge.io/), a rather influential computer algebra system of ancient lineage still in use today in more places than you might think.
> In order to show the steps, the calculator applies the same integration techniques that a human would apply. The program that does this has been developed over several years and is written in Maxima's own programming language. It consists of more than 17000 lines of code. When the integrand matches a known form, it applies fixed rules to solve the integral (e. g. partial fraction decomposition for rational functions, trigonometric substitution for integrands involving the square roots of a quadratic polynomial or integration by parts for products of certain functions). Otherwise, it tries different substitutions and transformations until either the integral is solved, time runs out or there is nothing left to try. The calculator lacks the mathematical intuition that is very useful for finding an antiderivative, but on the other hand it can try a large number of possibilities within a short amount of time. The step by step antiderivatives are often much shorter and more elegant than those found by Maxima.
Maxima ist absolutely great. It can be somewhat confusing, but it is actually quite advanced.
Calculating integrals is extremely hard (unlike calculating derivatives, which is very easy to do) and maxima comes with some of the more advanced and comprehensive strategies to solve integrals.
Shout out to another project by the same creator: https://www.derivative-calculator.net/
Both of these helped me through my undergrad physics degree, especially because of the step-by-step solutions. Without it I wouldn't have learned nearly as much about calculus.
Right? Its such a useful site that is regularly updated and just made by some guy (David Scherfgen) and not a big company trying to make money (E.g symbolab).
I really like the interactive function graph. Feels lightweight and snappy compared to the usual framework-driven solutions. I wish the author had gone into a bit more detail on how that works.
[+] [-] blobcode|1 year ago|reply
[+] [-] lupire|1 year ago|reply
> In order to show the steps, the calculator applies the same integration techniques that a human would apply. The program that does this has been developed over several years and is written in Maxima's own programming language. It consists of more than 17000 lines of code. When the integrand matches a known form, it applies fixed rules to solve the integral (e. g. partial fraction decomposition for rational functions, trigonometric substitution for integrands involving the square roots of a quadratic polynomial or integration by parts for products of certain functions). Otherwise, it tries different substitutions and transformations until either the integral is solved, time runs out or there is nothing left to try. The calculator lacks the mathematical intuition that is very useful for finding an antiderivative, but on the other hand it can try a large number of possibilities within a short amount of time. The step by step antiderivatives are often much shorter and more elegant than those found by Maxima.
[+] [-] kristopolous|1 year ago|reply
I wonder what those early versions were like. It's on lisp so it's feasibly still runnable without too much fussing around
[+] [-] constantcrying|1 year ago|reply
Calculating integrals is extremely hard (unlike calculating derivatives, which is very easy to do) and maxima comes with some of the more advanced and comprehensive strategies to solve integrals.
[+] [-] iillexial|1 year ago|reply
[+] [-] cjk2|1 year ago|reply
[+] [-] fragebogen|1 year ago|reply
[+] [-] mochito_bottle|1 year ago|reply
[+] [-] beckthompson|1 year ago|reply
[+] [-] CamperBob2|1 year ago|reply
[+] [-] ekiauhce|1 year ago|reply
[+] [-] abhinavstarts|1 year ago|reply