Resumo
The present paper shows that the sum of two binomial integrals, such as A ∫ x p (a + bx q)r dx + B ∫ x p (a + bx q)r dx, where A and B are real constants and p, q, r are rational numbers, can, in special cases, lead to elementary integrals, even if each by itself is not elementary. An example of the case considered is given by the integral ∫ x _____-___ 3 dx = 1/2 ∫ x-½ (x - 1)-⅓ dx - 6 √ x ³√(x - 1)4 = 1/3 ∫ x-½ (x - 1)-¾ dx On the rigth hand side of the last equality both integral are not elementary. But the use of integration by parts of one of them leads to the solution: ∫ x _____-___ 3 dx = x½ (x - 1)-⅓ + C. 6 √ x ³√(x - 1)4
Escola Superior de Agricultura «Luiz de Queiroz»
SUMMARY
The present paper shows that the sum of two binomial integrals, such as
A ∫ xp (a + bxq)r dx + B ∫ xp (a + bxq)r dx,
where A and B are real constants and p, q, r are rational numbers, can, in special cases, lead to elementary integrals, even if each by itself is not elementary. An example of the case considered is given by the integral
∫ x _____-___ 3 dx = 1/2 ∫ x-½ (x - 1)-⅓ dx -
6 √ x 3√(x - 1)4 = 1/3 ∫ x-½ (x - 1)-¾ dx
On the rigth hand side of the last equality both integral are not elementary. But the use of integration by parts of one of them leads to the solution:
∫ x _____-___ 3 dx = x½ (x - 1)-⅓ + C.
6 √ x 3√(x - 1)4
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LITERATURA CITADA
Recebido para publicação em 23 de março de 1960.
- CATUNDA, Omar - 1953 - Curso de Análise Matemática - III Parte. Editôra Bandeirantes, S. Paulo.
- POTRON, M. L' Abbé - L' Integrale de Différentielle Binome. Gauthier - Villars, Paris.
Um caso especial de integrais binômias
Datas de Publicação
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Publicação nesta coleção
10 Set 2012 -
Data do Fascículo
1960
Histórico
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Recebido
23 Mar 1960