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There are several web sites which have tables of integrals and integrals on demand. Wolfram Alpha can show results, and for some simpler expressions, also the intermediate steps of the integration. Wolfram Research also operates another online service, the Mathematica Online Integrator.
WolframAlpha (/ ˈ w ʊ l f. r əm-/ WUULf-rəm-) is an answer engine developed by Wolfram Research. [3] It is offered as an online service that answers factual queries by computing answers from externally sourced data.
In mathematics, the definite integral ∫ a b f ( x ) d x {\displaystyle \int _{a}^{b}f(x)\,dx} is the area of the region in the xy -plane bounded by the graph of f , the x -axis, and the lines x = a and x = b , such that area above the x -axis adds to the total, and that below the x -axis subtracts from the total.
Plot of the exponential integral function E n(z) with n=2 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D In mathematics, the exponential integral Ei is a special function on the complex plane .
A line integral (sometimes called a path integral) is an integral where the function to be integrated is evaluated along a curve. [42] Various different line integrals are in use. In the case of a closed curve it is also called a contour integral. The function to be integrated may be a scalar field or a vector field.
More generally, one can also consider integrands that have a known power-law singularity at x=0, for some real number >, leading to integrals of the form: + (). In this case, the weights are given [2] in terms of the generalized Laguerre polynomials:
In integral calculus, an elliptic integral is one of a number of related functions defined as the value of certain integrals, which were first studied by Giulio Fagnano and Leonhard Euler (c. 1750). Their name originates from their originally arising in connection with the problem of finding the arc length of an ellipse .
This integral follows from the general relation of the polylogarithm with the Hurwitz zeta function and a familiar integral representation of the latter. The polylogarithm may be quite generally represented by a Hankel contour integral ( Whittaker & Watson 1927 , § 12.22, § 13.13), which extends the Bose–Einstein representation to negative ...