Jump to navigation Jump to search This article is about mostly indefinite integrals in calculus. For a list of definite integrals, see List of integraltafeln PDF integrals.
Författare: Carl Naske.
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This article includes a list of references, but its sources remain unclear because it has insufficient inline citations. Integration is the basic operation in integral calculus. These tables were republished in the United Kingdom in 1823. Since 1968 there is the Risch algorithm for determining indefinite integrals that can be expressed in term of elementary functions, typically using a computer algebra system.
Other useful resources include Abramowitz and Stegun and the Bateman Manuscript Project. Both works contain many identities concerning specific integrals, which are organized with the most relevant topic instead of being collected into a separate table. Two volumes of the Bateman Manuscript are specific to integral transforms. 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. C is used for an arbitrary constant of integration that can only be determined if something about the value of the integral at some point is known. Thus, each function has an infinite number of antiderivatives.
These formulas only state in another form the assertions in the table of derivatives. C does not need to be the same on both sides of the singularity. 0 and the antiderivative becomes infinite there. 1 and 1, one would get the wrong answer 0. This however is the Cauchy principal value of the integral around the singularity.
See Integral of the secant function. This result was a well-known conjecture in the 17th century. For having a continuous antiderivative, one has thus to add a well chosen step function. There are some functions whose antiderivatives cannot be expressed in closed form. However, the values of the definite integrals of some of these functions over some common intervals can be calculated. A few useful integrals are given below.