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Laurie Rosatone Shannon Corliss Jonathan Cottrell Lucille Buonocore Barbara Russiello Melissa Edwards Lisa Sabatini Madelyn Lesure Sheena Goldstein © Denis Jr. PUBLISHER PROJECT EDITOR MARKETING MANAGER CONTENT MANAGER PRODUCTION EDITOR MEDIA EDITOR MEDIA PRODUCTION SPECIALIST TEXT AND COVER DESIGN PHOTO RESEARCHER COVER PHOTO NORMINTON Associate Professor of Mathematics Carleton University Ottawa, Ontario 冕 sin x dx ⫽ _ x ⫺ _ sin 2x ⫹ c 冕 cos x dx ⫽ _ x ⫹ _ sin 2x ⫹ c 冕 tan x dx ⫽ tan x ⫺ x ⫹ c 冕 cot x dx ⫽ ⫺cot x ⫺ x ⫹ c 冕 ln x dx ⫽ x ln x ⫺ x ⫹ c 冕 e sin bx dx 2ġ (arcsin x)⬘ ⫽ ᎏᎏ 兹1苶苶 ⫺苶x 2苶 1 (arccos x)⬘ ⫽ ⫺ ᎏᎏ 兹1苶苶 ⫺苶x 2苶 1 (arctan x)⬘ ⫽ ᎏ 1 ⫹ x2 1 (arccot x)⬘ ⫽ ⫺ ᎏ 1 ⫹ x2Ĭos bx dx eax ⫽ 2 (a cos bx ⫹ b sin bx) ⫹ c a ⫹ b2ĪDVANCED ENGINEERING MATHEMATICS ERWIN KREYSZIG Professor of Mathematics Ohio State University Columbus, OhioĮDWARD J. 冕 1x dx ⫽ ln 兩x兩 ⫹ c 冕 e dx ⫽ 1a e ⫹ c 冕 sin x dx ⫽ ⫺cos x ⫹ c 冕 cos x dx ⫽ sin x ⫹ c 冕 tan x dx ⫽ ⫺ln 兩cos x兩 ⫹ c 冕 cot x dx ⫽ ln 兩sin x兩 ⫹ c 冕 sec x dx ⫽ ln 兩sec x ⫹ tan x兩 ⫹ c 冕 csc x dx ⫽ ln 兩csc x ⫺ cot x兩 ⫹ c 1 dx x 冕ᎏ ⫽ ᎏ arctan ᎏ ⫹ c a x ⫹a a ax (x n)⬘ ⫽ nxnⴚ1 (e x)⬘ ⫽ e x (e ax)⬘ ⫽ ae ax (a x)⬘ ⫽ a x ln a (sin x)⬘ ⫽ cos x (cos x)⬘ ⫽ ⫺sin x (tan x)⬘ ⫽ sec2 x (cot x)⬘ ⫽ ⫺csc2 x (sinh x)⬘ ⫽ cosh x (cosh x)⬘ ⫽ sinh x 1 (ln x)⬘ ⫽ ᎏ x loga e (loga x)⬘ ⫽ ᎏ x 冕 uv⬘ dx ⫽ uv ⫺ 冕 u⬘v dx (by parts) 冕 x dx ⫽ nx ⫹ 1 ⫹ c (n ⫽ ⫺1) n⫹1
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08854, website at Differentiation (cu)⬘ ⫽ cu⬘ See also AN American National Standard, ASTM/IEEE Standard Metric Practice, Institute of Electrical and Electronics Engineers, Inc. gallon ⫽ 4 quarts (liq) ⫽ 8 pints (liq) ⫽ 128 fl oz ⫽ 3785.4118 cm3 1 British Imperial and Canadian gallon ⫽ 1.200949 U.S. The mks system is also known as the International System of Units (abbreviated SI ), and the abbreviations sec (instead of s), gm (instead of g), and nt (instead of N) are also used.ġ statute mile (mi) ⫽ 5280 ft ⫽ 1.609344 kmġ nautical mile ⫽ 6080 ft ⫽ 1.853184 km 1 acre ⫽ 4840 yd2 ⫽ 4046.8564 m2ġ fluid ounce ⫽ 1/128 U.S. Some Important Conversion Factors The most important systems of units are shown in the table below.