HOW TO ENTER INPUT

This page outlines some important points for writing integrands. The Wolfram Mathematica Online Integrator is powered by webMathematica, so it expects input to be in Mathematica syntax. It can also parse many expressions when they are not in exactly the right form, so people who are unfamiliar with Mathematica syntax details will not usually encounter problems. However, we recommend you become familiar with the material on this page for best results.

Basic Rules

Example: Type Sqrt[Sin[x]] for the square root of the sine of x.

Arguments of functions are put inside square brackets.

Multiplication is indicated by a space.

Elementary and Operations Functions

Basic Arithmetic Operations

 a + b plus a - b minus a b or a*b times a/b divide a^b power Sqrt[a] square root

Mathematical Constants
 Pi 3.14159... Degree degree I i E e, 2.71828... GoldenRatio golden ratio, 1.61803... EulerGamma Euler's constant, 0.57721... Catalan Catalan's constant, 0.91596... StieltjesGamma[n] Stieltjes constants

Trigonometric and Exponential Functions
 Sin[x], Cos[x], Tan[x], Csc[x], Sec[x], Cot[x] trigonometric functions (with arguments in radians) ArcSin[x], ArcCos[x], ArcTan[x], ArcTan[x,y], ArcCsc[x], ArcSec[x], ArcCot[x] inverse trigonometric functions (giving results in radians) Exp[x] or E^x exponential function Log[x] natural logarithm Log[b, x] logarithm of x to the base b Sinh[x], Cosh[x], Tanh[x], Csch[x], Sech[x], Coth[x] hyperbolic functions ArcSinh[x], ArcCosh[x], ArcTanh[x], ArcCsch[x], ArcSech[x], ArcCoth[x] inverse hyperbolic functions

Higher Mathematical Functions

Mathematica includes over 500 higher mathematical functions, including almost all the functions of mathematical physics.

Names of functions are usually complete English words.

Mathematical functions that are usually referred to by a person's name have names in Mathematica of the form PersonSymbol. For example, the Legendre polynomials are denoted by LegendreP[n, x].

If the standard notation for a mathematical function involves both subscripts and superscripts, the subscript is given before the superscript in the Mathematica form. For example, the associated Legendre polynomials, which are usually written as , are denoted as LegendreP[n, m, x].