An Elementary Treatise On Curves, Functions, And Forces
An Elementary Treatise On Curves, Functions, And Forces
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In our eReader you can find the full English version of the book. Read An Elementary Treatise On Curves, Functions, And Forces Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book An Elementary Treatise On Curves, Functions, And Forces
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Integrate — ^ . Ans. \os.^ x.
^ X log. X ^ 50. Problem. To find the value of the definite in- tegral n. (-\og. X)i (419) in which n is an integer greater than — 2.
Solution. First. In this case, (408-410) give /. X=I, F. X^^x, f. F. Xz=x', (420) /. (- log. X. Y = X (- log. Xf + ^f. (- log. X)^-' (421) in which when x =1 0, or = ], (422) the first term of the second member vanishes as in example 2 of B. II. § 109, so that the required integral becomes In-i-^og-^-'- (423) By this process, then, t...he exponent of ( — log. X) is dimin- ished by unity ; and a continued repetition of it gives for the value of (419) i(i-')(i-"") (l-''+^)f:-i-^o, .. Mm n in which h is an integer not greater than - -f- 1.
«5> 50. ] LOGARITHMIC FUNCTIONS. 105 Logarithmic definite integrals.
Secondly. When n is even, let h — ^n (425) and (424) gives /i. (-Iog. 2;)'^=1. 2. 3 h. (426) Thirdly. When n is odd, and positive, let h = ln + i, (427) and (424) gives /■. (-log.^)'-*= (A_J)(A_|)... |. J/.. (_Iog..
What to read after An Elementary Treatise On Curves, Functions, And Forces?
You can find similar books in the "Read Also" column, or choose other free books by Benjamin Peirce to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Integrate — ^ . Ans. \os.^ x.
^ X log. X ^ 50. Problem. To find the value of the definite in- tegral n. (-\og. X)i (419) in which n is an integer greater than — 2.
Solution. First. In this case, (408-410) give /. X=I, F. X^^x, f. F. Xz=x', (420) /. (- log. X. Y = X (- log. Xf + ^f. (- log. X)^-' (421) in which when x =1 0, or = ], (422) the first term of the second member vanishes as in example 2 of B. II. § 109, so that the required integral becomes In-i-^og-^-'- (423) By this process, then, t...he exponent of ( — log. X) is dimin- ished by unity ; and a continued repetition of it gives for the value of (419) i(i-')(i-"") (l-''+^)f:-i-^o, .. Mm n in which h is an integer not greater than - -f- 1.
«5> 50. ] LOGARITHMIC FUNCTIONS. 105 Logarithmic definite integrals.
Secondly. When n is even, let h — ^n (425) and (424) gives /i. (-Iog. 2;)'^=1. 2. 3 h. (426) Thirdly. When n is odd, and positive, let h = ln + i, (427) and (424) gives /■. (-log.^)'-*= (A_J)(A_|)... |. J/.. (_Iog..
What to read after An Elementary Treatise On Curves, Functions, And Forces?
You can find similar books in the "Read Also" column, or choose other free books by Benjamin Peirce to read onlineMoreLess
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