An Elementary Treatise On the Differential And Integral Calculus With Numerous
An Elementary Treatise On the Differential And Integral Calculus With Numerous
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To quickly assess the difficulty of the text, read a short excerpt:
) •'• J'^^J'^^^ ^^^ x) = a log X.
♦ The arbitrary constant is not mentioned since its addition is always under- stood, and in tiie following integrals it will be omitted, as it can always be supplied when necessary.
EXAMPLES. 241 Hence, ivhenever a differential is a fraction whose mi'jnerator is the product of a constant by the differ- ential of the denominator, its integral is the product of the constant by the Maperian logarithm of the denominator.
EXAMPLES.
1. To integrate dy = ax^dx.
y = J ...axhlx =z J a • x^ • dx = --• [by (3)].
2. To integrate dy = {a -\- bx^Yxhlx.
The differential of the quantity within the parenthesis being 16x^dx, we write y = f-h{a + 5^y ^^xHx = (^^1^1'. [by (3)1 This example might also be integrated by expanding the quantity within the ])arenthesis, and integrating each term separately by (1), but the process would be more lengthy than the one employed.
3. To integrate dy = a (nx^ + bx^)i 2xdx + Ux^ {ax^ + b^)^ dx.
y = fla {ax''' -f ^a:^)^ 2xdx + dbx^ (ax^ + bx^)^ dx] = f{ax^ + bx^)^ {2ax + ^bx^) dx = | (ax^ + bx^f^ [by {3)].
What to read after An Elementary Treatise On the Differential And Integral Calculus With Numerous?
You can find similar books in the "Read Also" column, or choose other free books by Edward a Edward Albert Bowser to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
) •'• J'^^J'^^^ ^^^ x) = a log X.
♦ The arbitrary constant is not mentioned since its addition is always under- stood, and in tiie following integrals it will be omitted, as it can always be supplied when necessary.
EXAMPLES. 241 Hence, ivhenever a differential is a fraction whose mi'jnerator is the product of a constant by the differ- ential of the denominator, its integral is the product of the constant by the Maperian logarithm of the denominator.
EXAMPLES.
1. To integrate dy = ax^dx.
y = J ...axhlx =z J a • x^ • dx = --• [by (3)].
2. To integrate dy = {a -\- bx^Yxhlx.
The differential of the quantity within the parenthesis being 16x^dx, we write y = f-h{a + 5^y ^^xHx = (^^1^1'. [by (3)1 This example might also be integrated by expanding the quantity within the ])arenthesis, and integrating each term separately by (1), but the process would be more lengthy than the one employed.
3. To integrate dy = a (nx^ + bx^)i 2xdx + Ux^ {ax^ + b^)^ dx.
y = fla {ax''' -f ^a:^)^ 2xdx + dbx^ (ax^ + bx^)^ dx] = f{ax^ + bx^)^ {2ax + ^bx^) dx = | (ax^ + bx^f^ [by {3)].
What to read after An Elementary Treatise On the Differential And Integral Calculus With Numerous?
You can find similar books in the "Read Also" column, or choose other free books by Edward a Edward Albert Bowser to read onlineMoreLess
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