From the INTRODUCTION. THE following table of integrals has been drawn up with the hope of lessening the labour often involved in the integration of elementary functions. The list includes all the ordinary standard integrals and formula of reduction, arranged compactly, so as to allow of easy reference. Although the tables occupy less space than some which are in existence, yet it is hoped that the present set may prove no less useful in practical work; for example, it proved possible in many instances to condense three or ...
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From the INTRODUCTION. THE following table of integrals has been drawn up with the hope of lessening the labour often involved in the integration of elementary functions. The list includes all the ordinary standard integrals and formula of reduction, arranged compactly, so as to allow of easy reference. Although the tables occupy less space than some which are in existence, yet it is hoped that the present set may prove no less useful in practical work; for example, it proved possible in many instances to condense three or more separate formulae into a single reduction formula; and it is hardly necessary to point out that a given result can be found more quickly in a short than in a long table. A few other useful forms, such as (57), (58), have been added, which do not appear in the ordinary textbooks: and in selecting definite integrals, preference has been given to examples which occur in potential-theory and other branches of Applied Mathematics. Some numerical examples have been added to illustrate the general formulae, but it is not intended that these should be regarded in any way as replacing the sets of examples provided by books on the Calculus. Methods of approximate integration - by Simpson's formulae and the plauimeter- are briefly formulated in the last two sections.
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