A Treatise on Infinitesimal Calculus ... |
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Page 31
... Substituting therefore in ( 34 ) , F ( x ) f ( x ) ( a1 ) y ' ( a1 ) 1 " ( a1 ) 1 = + + ( x —α1 ) m 1 ( x - α1 ) m - 1 1.2 ( x - a1 ) -2 + ... 4m - 1 ( a1 ) 1 F ( am + 1 ) 1 + + 1.2.3 ... ( m - 1 ) x — a1 + f ( am + 1 ) x - am + ...
... Substituting therefore in ( 34 ) , F ( x ) f ( x ) ( a1 ) y ' ( a1 ) 1 " ( a1 ) 1 = + + ( x —α1 ) m 1 ( x - α1 ) m - 1 1.2 ( x - a1 ) -2 + ... 4m - 1 ( a1 ) 1 F ( am + 1 ) 1 + + 1.2.3 ... ( m - 1 ) x — a1 + f ( am + 1 ) x - am + ...
Page 49
... ( a2 — x2 ) 1 dx . Let u = ( a2 — x2 ) , --- -xdx – Svdu . dvdx ; ( 78 ) ... du = ( a2 — x2 ) PRICE , VOL . II . v = x . H Substituting which in the formula ( 78 ) , - 39. ] 49 IRRATIONAL ALGEBRAICAL FUNCTIONS . Integration.
... ( a2 — x2 ) 1 dx . Let u = ( a2 — x2 ) , --- -xdx – Svdu . dvdx ; ( 78 ) ... du = ( a2 — x2 ) PRICE , VOL . II . v = x . H Substituting which in the formula ( 78 ) , - 39. ] 49 IRRATIONAL ALGEBRAICAL FUNCTIONS . Integration.
Page 50
Bartholomew Price. Substituting which in the formula ( 78 ) , - x2 dx [ ( a2_x2 ) 3 dx = x ( a2 — x2 ) * + f ( a2 = 29 ) ¢ - Then , adding and subtracting a2 in the numerator of the last quantity , and writing the fraction in two parts ...
Bartholomew Price. Substituting which in the formula ( 78 ) , - x2 dx [ ( a2_x2 ) 3 dx = x ( a2 — x2 ) * + f ( a2 = 29 ) ¢ - Then , adding and subtracting a2 in the numerator of the last quantity , and writing the fraction in two parts ...
Page 54
... substituting a + bx ” = za ; Р q is an integer , by substituting b + ax¬ " = z ? ̧ * 45. ] Examples of the two preceding articles . fx ( a + bx ) 3 dx . Ex . 1 . In this case m = 1 , n = 1.0 3 m + 1 = q 2 ' n = 2 , and is integral . Let ...
... substituting a + bx ” = za ; Р q is an integer , by substituting b + ax¬ " = z ? ̧ * 45. ] Examples of the two preceding articles . fx ( a + bx ) 3 dx . Ex . 1 . In this case m = 1 , n = 1.0 3 m + 1 = q 2 ' n = 2 , and is integral . Let ...
Page 63
... Substituting which in ( 99 ) , and adding and reducing , x dx ( a + bx + cx2 ) 1 = x " -2 dx 2 = -1 ( a + bx + ca2 ) * _ ^ -1 a√ ( a + bx + ca2 ) b nc n C 2n - 1b xn - 1dx - 2n cJ ( a + bx + cx2 ) ; ( 100 ) so that the last integrals ...
... Substituting which in ( 99 ) , and adding and reducing , x dx ( a + bx + cx2 ) 1 = x " -2 dx 2 = -1 ( a + bx + ca2 ) * _ ^ -1 a√ ( a + bx + ca2 ) b nc n C 2n - 1b xn - 1dx - 2n cJ ( a + bx + cx2 ) ; ( 100 ) so that the last integrals ...
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A Treatise on Infinitesimal Calculus: Containing Differential and Integral ... Bartholomew Price No preview available - 2015 |
Common terms and phrases
a₁ a₂ angle application axis Beta-function bx dx consequently convergent series coordinates cosec cx² cycloid definite integral denoted determined differential double integral dx a² dx dx dx dy dx Ex dx² dy dx dy² e-ax element-function ellipse equal evaluation expressed find the area finite and continuous fraction function Gamma-function geometrical given Hence infinite infinitesimal infinitesimal element Integral Calculus intrinsic equation involute left-hand member length let us suppose limits of integration multiple integrals plane curve polar coordinates preceding proper fraction radius range of integration replaced result right-hand member subject-variable substituting surface symbols theorem tion values variable x-integration x₁ x²)¹ x²)³ αξ πα