When the integrand matches a known form, it applies fixed rules to solve the integral (e. g. It consists of more than 17000 lines of code. The program that does this has been developed over several years and is written in Maxima's own programming language. In order to show the steps, the calculator applies the same integration techniques that a human would apply. That's why showing the steps of calculation is very challenging for integrals. The antiderivative is computed using the Risch algorithm, which is hard to understand for humans. Maxima's output is transformed to LaTeX again and is then presented to the user. Maxima takes care of actually computing the integral of the mathematical function. This time, the function gets transformed into a form that can be understood by the computer algebra system Maxima. When the "Go!" button is clicked, the Integral Calculator sends the mathematical function and the settings (variable of integration and integration bounds) to the server, where it is analyzed again. MathJax takes care of displaying it in the browser. This allows for quick feedback while typing by transforming the tree into LaTeX code. The parser is implemented in JavaScript, based on the Shunting-yard algorithm, and can run directly in the browser. The Integral Calculator has to detect these cases and insert the multiplication sign. A specialty in mathematical expressions is that the multiplication sign can be left out sometimes, for example we write "5x" instead of "5*x". In doing this, the Integral Calculator has to respect the order of operations. It transforms it into a form that is better understandable by a computer, namely a tree (see figure below). We can also simplify algebraic expressions by factoring and solving all applicable operations, especially multiplication and division.For those with a technical background, the following section explains how the Integral Calculator works.įirst, a parser analyzes the mathematical function. Then, we combine the like terms, that is, the terms that have the same variable raised to the same power: 2 x²+4 x+2. To simplify algebraic expressions, we can use the distributive property to remove parentheses or other grouping signs to then combine like terms.įor example, to simplify the expression 2 x( x+3)-2 x+2, we have to start by using the distributive property to remove the parentheses: 2 x²+6 x-2 x+2. Simplifying algebraic expressions means writing this expression in its simplest possible form. For example, the expression 1/(3x^2) indicates that the entire expression inside the parentheses goes into the denominator of the fraction. The use of parentheses is recommended to write the expression properly.
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