English Title

A succinct integration of the most memorable integral formula ∫ ∂z/((3±zz)∙(1±3zz)1/3)

Authors

Leonhard Euler

Enestrom Number

695

Fuss Index

215

Original Language

Latin

Published as

Journal article

Published Date

1797

Written Date

1777

Archive Notes

Euler used a cube root in the title of this work, rather than the 1/3 power indicated in the Euler Archive's listed title.

Content Summary

The integrals in the title are calculated with some very clever substitutions and imaginative use of imaginaries. Seeing that this method is not very obvious, Euler proceeds to rederive the results (with fewer details) in a more natural way, but nonetheless judges the former method to be better. The paper concludes with some remarks affirming that no matter how one calculates them, one must use imaginary quantities.

Original Source Citation

Nova Acta Academiae Scientiarum Imperialis Petropolitanae, Volume 10, pp. 20-26.

Opera Omnia Citation

Series 1, Volume 19, pp.287-296.

Record Created

2018-09-25

Included in

Mathematics Commons

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