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Wolfram Mathematica Online Integrator

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.

Names of functions start with capital letters.

Arguments of functions are put inside square brackets.

Multiplication is indicated by a space.

Elementary and Operations Functions

Basic Arithmetic Operations

Links in the first column will take you to more information about a particular function in the online Mathematica Documentation Center. Links in the second column will take you to more information about the function in MathWorld.

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].

Combinatorial polynomials

Orthogonal polynomials

Gamma and related functions

Zeta and related functions

Exponential Integral and related functions

Error function and related functions

Bessel functions

Legendre and related functions

Confluent hypergeometric functions

Hypergeometric functions and generalizations

ProductLog function

Elliptic integrals

Elliptic functions

Mathieu and related functions


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