Common Derivatives And Integrals
Transcription
Common Derivatives And Integrals
Common Derivatives And Integrals Integral Rules Derivative Rules d (sin u) dx = cos u du dx Z sin u du = ¡ cos u + C d (cos u) dx = ¡ sin u du dx Z cos u du = d (tan u) dx = Z tan u du = ¡ ln j cos uj + C d (csc u) dx = ¡ csc u cot u du dx Z csc u du = ¡ ln j csc u + cot uj + C du sec u tan u dx Z sec u du = ln j sec u + tan uj + C Z cot u du = ln j sin uj + C 1 du u dx Z sec2 u du = tan u + C 1 du u dx Z csc2 u du = ¡ cot u + C Z sec u tan u du = Z csc u cot u du = ¡ csc u + C Z 1 du u = ln juj + C Z eu du = eu + C = µ sec2 u du dx d (sec u) dx = d (cot u) dx du = ¡ csc u dx d (ln u) dx 2 = d (ln juj) dx = d u (e ) dx = eu d (loga u) = dx µ d u (a ) dx du (ln a) au dx = du dx 1 ln a ¶ 1 du u dx Z u a du sin u + C sec u + C ¶ 1 au + C ln a